{"id":3978,"date":"2021-01-30T12:25:48","date_gmt":"2021-01-30T12:25:48","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3978"},"modified":"2022-03-23T19:36:10","modified_gmt":"2022-03-23T19:36:10","slug":"laws-of-force","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/laws-of-force\/","title":{"rendered":"\u09ac\u09b2\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf (Laws of Force)"},"content":{"rendered":"<h2><b>\u09ac\u09b2\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af (Converse law of triangle law of forces)\u00a0<\/b><\/h2>\n<p><b>\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (statement): <\/b><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09a5\u09be\u0995\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u098f\u0995\u0987\u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u0995\u09cb\u09a8\u09cb \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<p><b>\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (Proof): <\/b><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <\/span><span style=\"font-weight: 400;\">OX,\u00a0OY,\u00a0OZ\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u0986\u099b\u09c7\u0964\u00a0<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-3983 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/18.1-2-1024x654.png\" alt=\"Converse law of triangle law of forces\" width=\"1024\" height=\"654\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/18.1-2-1024x654.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/18.1-2-300x192.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/18.1-2-768x491.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/18.1-2.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">OX<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">OY<\/span><span style=\"font-weight: 400;\"> \u09a5\u09c7\u0995\u09c7 \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u0995\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">OA<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">OB<\/span><span style=\"font-weight: 400;\"> \u0985\u0982\u09b6 \u0995\u099f\u09c7 \u09a8\u09bf\u0987 \u09af\u09c7\u09a8 \u0989\u09b9\u09be\u09b0\u09be <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u0995\u09c7 (\u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7) \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09c7\u0964 <\/span><span style=\"font-weight: 400;\">OACB<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995\u099f\u09bf \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09af\u09cb\u0997 \u0995\u09b0\u09bf\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09c7, \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u099f\u09bf <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u099f\u09bf \u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964 \u0986\u09ac\u09be\u09b0 <\/span><span style=\"font-weight: 400;\">OB\u2225AC<\/span><span style=\"font-weight: 400;\"> \u09b9\u0993\u09df\u09be\u09df <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u099f\u09bf \u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">AC<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09a4\u098f\u09ac <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">OAC<\/span><span style=\"font-weight: 400;\"> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09be\u09b9\u09c1 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">OA,\u00a0AC\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09b2\u0964\u00a0<\/span><\/p>\n<p><b>\u09ac\u09bf\u0995\u09b2\u09cd\u09aa \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (\u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf) (Alternative way of proof (vector method)): <\/b><\/p>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <\/span><span style=\"font-weight: 400;\">OX,\u00a0OY,\u00a0OZ\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u0986\u099b\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">OX<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">OY<\/span><span style=\"font-weight: 400;\"> \u09a5\u09c7\u0995\u09c7 \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u0995\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">OA<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">OB<\/span><span style=\"font-weight: 400;\"> \u0985\u0982\u09b6 \u0995\u099f\u09c7 \u09a8\u09bf\u0987 \u09af\u09c7\u09a8 \u0989\u09b9\u09be\u09b0\u09be <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u0995\u09c7 (\u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7) \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09c7\u0964 <\/span><span style=\"font-weight: 400;\">OACB<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995\u099f\u09bf \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u0995\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09af\u09cb\u0997 \u0995\u09b0\u09bf\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\overrightarrow{O A}=P<\/span> <\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982<\/span> <span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\overrightarrow{O B}=Q<\/span><\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">O B \\| A C<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">O B=A C \\quad \\therefore \\overrightarrow{A C}=Q<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P+Q=\\overrightarrow{O A}+\\overrightarrow{O B}=\\overrightarrow{O C}<\/span><\/span><span style=\"font-weight: 400;\"> \u00a0 [\u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09b0\u09df\u09c7\u099b\u09c7\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore P+Q+R=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\overrightarrow{O C}+R=0<\/span> <\/span><span style=\"font-weight: 400;\"> \u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">R=-\\overrightarrow{O C}=\\overrightarrow{C O}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234<\/span> <span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a4\u09cd\u09b0\u09df\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">OAC<\/span><span style=\"font-weight: 400;\"> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 <\/span><span style=\"font-weight: 400;\">OA,\u00a0AC\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ae\u09be\u09a8\u09c7, \u09a6\u09bf\u0995\u09c7 \u0993 \u098f\u0995\u0987\u0995\u09cd\u09b0\u09ae\u09c7 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n<h2><b>\u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0 (Perpendicular triangle law of forces)<\/b><\/h2>\n<p><b>\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (statement): <\/b><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09af\u09a6\u09bf \u0995\u09cb\u09a8\u09cb \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09be\u09b9\u09c1\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u098f\u09ac\u0982 \u09a6\u09bf\u0995 \u0986\u09a8\u09c1\u09b7\u0999\u09cd\u0997\u09bf\u0995 \u09ac\u09be\u09b9\u09c1 \u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac (\u09b8\u0995\u09b2 \u09ac\u09b2\u09c7\u09b0 \u09a6\u09bf\u0995 \u09b9\u09af\u09bc \u09ac\u09b9\u09bf\u09b0\u09cd\u09ae\u09c1\u0996\u09c0 \u0985\u09a5\u09ac\u09be \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ae\u09c1\u0996\u09c0) \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09ad\u09be\u09b0\u09b8\u09be\u09ae\u09cd\u09af \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0995\u09c7 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09b0\u09c7\u0996\u09c7 \u09b8\u09ac\u0997\u09c1\u09b2\u09bf \u09ac\u09b2\u0995\u09c7 \u098f\u0995\u0987 \u09b8\u09be\u09a5\u09c7 \u098f\u0995 \u09b8\u09ae\u0995\u09cb\u09a3\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\left(90^{\\circ}\\right)<\/span> <\/span><span style=\"font-weight: 400;\">\u0986\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09b2\u09c7, \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u098f\u0995\u099f\u09bf \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u09ac\u09be\u09b9\u09c1\u09a4\u09cd\u09b0\u09af\u09bc \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ac\u09b2\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09c7\u0964<\/span><\/p>\n<h2><b>\u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09b2\u09be\u09ae\u09bf\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af (Lami&#8217;s Theorem of Equilibrium)<\/b><\/h2>\n<p><b>\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (statement): <\/b><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09ae\u09a4\u09b2\u09c0\u09df \u09ac\u09b2 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09a5\u09be\u0995\u09b2\u09c7, \u09a4\u09be\u09a6\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0985\u09aa\u09b0 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09c7\u0996\u09be\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cb\u09a3\u09c7\u09b0 \u09b8\u09be\u0987\u09a8\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964\u00a0<\/span><\/p>\n<p><b>\u09aa\u09cd\u09b0\u09ae\u09be\u09a3: \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf (Proof: Vector method): <\/b><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">OX,\u00a0OY\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">OZ<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09b8\u09ae\u09a4\u09b2\u09c0\u09df \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09b0\u09df\u09c7\u099b\u09c7\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-3984 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/19.1-1024x655.png\" alt=\"Lami's Theorem of Equilibrium\" width=\"1024\" height=\"655\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/19.1-1024x655.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/19.1-300x192.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/19.1-768x491.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/19.1.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin Y O Z}=\\frac{Q}{\\sin Z O X}=\\frac{R}{\\sin X O Y}<\/span><\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09b0\u09df\u09c7\u099b\u09c7, \u0995\u09be\u099c\u09c7\u0987-<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P+Q+R=0<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{R} \\times(P+Q+R)=0<\/span><\/span><span style=\"font-weight: 400;\"> [\u0989\u09ad\u09df \u09aa\u0995\u09cd\u09b7\u09c7 R \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0997\u09c1\u09a3\u09a8 \u0995\u09b0\u09c7] <span class=\"katex-eq\" data-katex-display=\"false\"> \\ldots(i)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{R} \\times P+R \\times Q+R \\times R=0<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{R} \\times P-Q \\times R=0 \\quad[\\because R \\times R=0<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">R \\times Q=-Q \\times R]<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">|R \\times P|=|Q \\times R|<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">|R P \\sin Z O X \\hat{n}|=|Q R \\sin Y O Z \\hat{n}|<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u00a0 [\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{n}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u0995\u09be\u09b0\u09c0 \u09b8\u09ae\u09a4\u09b2\u09c7\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u098f\u0995\u0995<\/span><span style=\"font-weight: 400;\">\u00a0\u09ad\u09c7\u0995\u09cd\u099f\u09b0]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">R P \\sin Z O X=Q R \\sin Y O Z<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P \\sin Z O X=Q \\sin Y O Z<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\frac{P}{\\sin Y O Z}=\\frac{Q}{\\sin Z O X} \\quad \\ldots\u00a0\\ldots (ii)<\/span><\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">i<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\"> \u09a8\u0982 \u0995\u09c7 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0997\u09c1\u09a8\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{Q}{\\sin Z O X}=\\frac{R}{\\sin X O Y} \\quad \\ldots\u00a0\\ldots (i i i)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">ii<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">iii<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\"> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin Y O Z}=\\frac{Q}{\\sin Z O X}=\\frac{R}{\\sin X O Y}<\/span><\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0985\u09aa\u09b0 \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09c7\u0996\u09be\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cb\u09a3\u09c7\u09b0 \u09b8\u09be\u0987\u09a8\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964\u00a0<\/span><\/p>\n<h3><b>\u09ac\u09bf\u0995\u09b2\u09cd\u09aa \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (\u099c\u09cd\u09af\u09be\u09ae\u09bf\u09a4\u09bf\u0995 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf) (Alternative proof (Geometric method))<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09ae\u09a4\u09b2\u09c0\u09af\u09bc <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ae\u09be\u09a8\u09c7\u09b0 \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">OX,\u00a0OY\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">OZ<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2 \u09b9\u09af\u09bc\u09c7 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u0986\u099b\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7,\u00a0 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin Y O Z}=\\frac{Q}{\\sin Z O X}=\\frac{R}{\\sin X O Y}<\/span><\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-3985 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/20.1-2-1024x637.png\" alt=\"Lami's Theorem of Equilibrium\" width=\"1024\" height=\"637\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/20.1-2-1024x637.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/20.1-2-300x187.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/20.1-2-768x477.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/20.1-2.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/> <span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">OX<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">OY<\/span><span style=\"font-weight: 400;\"> \u09a5\u09c7\u0995\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u0995\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09c7 <\/span><span style=\"font-weight: 400;\">OA<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">OB<\/span><span style=\"font-weight: 400;\"> \u09b0\u09c7\u0996\u09be\u0982\u09b6 \u0995\u09c7\u099f\u09c7 \u09a8\u09c7\u0987 \u09af\u09c7\u09a8 \u098f\u09b0\u09be \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09c7\u0964 <\/span><span style=\"font-weight: 400;\">OACB<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995\u099f\u09bf \u09aa\u09c2\u09b0\u09cd\u09a3 \u0995\u09b0\u09bf\u0964 <\/span><span style=\"font-weight: 400;\">O,\u00a0C\u00a0<\/span><span style=\"font-weight: 400;\">\u09af\u09cb\u0997 \u0995\u09b0\u09bf\u0964 \u09ac\u09b2\u09c7\u09b0 \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">OC<\/span><span style=\"font-weight: 400;\"> \u0995\u09b0\u09cd\u09a3 \u09a6\u09cd\u09ac\u09be\u09b0\u09be <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09df\u0964 \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09a5\u09be\u0995\u09c7 \u0995\u09be\u099c\u09c7\u0987 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u099f\u09bf \u0985\u09ac\u09b6\u09cd\u09af\u0987 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0\u00a0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09b0\u09c7\u0996\u09be\u0982\u09b6 \u09a6\u09cd\u09ac\u09be\u09b0\u09be <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09ac\u09c7\u0964 \u0986\u09ac\u09be\u09b0 <\/span><span style=\"font-weight: 400;\">OACB<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u09ac\u09b2\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">A C=O B=Q<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7\u09b9\u09c7\u09a4\u09c1, \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b2\u09a4\u09cd\u09b0\u09df \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u0986\u099b\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u099a\u09bf\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span><span style=\"font-weight: 400;\">OAC<\/span><span style=\"font-weight: 400;\"> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 <\/span><span style=\"font-weight: 400;\">OA,\u00a0AC\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf\u0995\u09c7 \u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7\u0964<\/span><\/p>\n<h2><b>\u09b2\u09be\u09ae\u09bf\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09aa\u09cd\u09b0\u09a4\u09bf\u099c\u09cd\u099e\u09be (Converse of Lami&#8217;s Theorem)<\/b><b>\u00a0<\/b><\/h2>\n<p><b>\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (Statement):<\/b><span style=\"font-weight: 400;\"> \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09ae\u09a4\u09b2\u09c0\u09af\u09bc \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995\u099f\u09bf\u09b0 \u09ae\u09be\u09a8 \u0985\u09aa\u09b0 \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cb\u09a3\u09c7\u09b0 \u09b8\u09be\u0987\u09a8\u09c7\u09b0\u00a0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u09b9\u09b2\u09c7 \u098f\u09ac\u0982 \u0995\u09cb\u09a8\u099f\u09bf\u0987 \u0985\u09aa\u09b0 \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8 \u09a8\u09be \u09b9\u09b2\u09c7, \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09ac\u09c7\u0964<\/span><\/p>\n<p><b>\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (Proof):<\/b> <span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span><span style=\"font-weight: 400;\">P,\u00a0Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09ae\u09a4\u09b2\u09c0\u09df \u09ac\u09b2 <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">OX,\u00a0OY\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">OZ<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be \u0995\u09b0\u09c7 \u09af\u09c7\u09a8\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin Y O Z}=\\frac{Q}{\\sin Z O X}=\\frac{R}{\\sin X O Y}<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">\\cdots \\cdots \\cdots(i)<\/span><br \/>\n<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09c7, <\/span><span style=\"font-weight: 400;\">OX<\/span><span style=\"font-weight: 400;\"> \u09b9\u09a4\u09c7 <\/span><span style=\"font-weight: 400;\">OA<\/span><span style=\"font-weight: 400;\"> \u0985\u0982\u09b6 \u0995\u09c7\u099f\u09c7 \u09a8\u09bf\u0987 \u09af\u09c7\u09a8 <\/span><span style=\"font-weight: 400;\">OA<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u099f\u09bf \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 <\/span><span style=\"font-weight: 400;\">ZO<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u098f\u09b0\u09c2\u09aa\u09c7 <\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09ac\u09b0\u09cd\u09a7\u09bf\u09a4 \u0995\u09b0\u09bf \u09af\u09c7\u09a8 <\/span><span style=\"font-weight: 400;\">AC<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 <\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\"> \u09a4\u09c7 \u099b\u09c7\u09a6 \u0995\u09b0\u09c7 \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{AC} \\| O B<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09af\u09bc\u0964 <\/span><span style=\"font-weight: 400;\">OACB<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u0997\u09a0\u09a8 \u0995\u09b0\u09bf\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-3986 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/21.1-2-1024x637.png\" alt=\"Converse of Lami's Theorem\" width=\"1024\" height=\"637\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/21.1-2-1024x637.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/21.1-2-300x187.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/21.1-2-768x477.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/21.1-2.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\triangle O A C<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{O A}{\\sin O C A}=\\frac{A C}{\\sin C O A}=\\frac{C O}{\\sin O A C}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{O A}{\\sin C O Y}=\\frac{A C}{\\sin (\\pi-Z O X)}=\\frac{C O}{\\sin (\\pi-C A X)}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{O A}{\\sin (\\pi-Y O Z)}=\\frac{A C}{\\sin Z O X}=\\frac{C O}{\\sin C A X}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{O A}{\\sin Y O Z}=\\frac{A C}{\\sin Z O X}=\\frac{C O}{\\sin X O Y} \\quad \\ldots\u00a0\\ldots (ii)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">i<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">ii<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\"> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{O A}=\\frac{Q}{A C}=\\frac{R}{C O} \\quad \\ldots\u00a0\\ldots (i i i)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 <\/span><span style=\"font-weight: 400;\">OA<\/span><span style=\"font-weight: 400;\"> \u09b0\u09c7\u0996\u09be\u0982\u09b6 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995\u09c7 P \u09ac\u09b2 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09c7, \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">P=O A<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09be\u09b9\u09b2\u09c7 <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">iii<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09b9\u09a4\u09c7 \u09aa\u09be\u0987, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">Q=A C<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">R=C O<\/span><\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 \u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">OAC<\/span><span style=\"font-weight: 400;\"> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 <\/span><span style=\"font-weight: 400;\">OA,\u00a0AC\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\"> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09df\u09c7\u099b\u09c7\u0964 \u0985\u09a4\u098f\u09ac \u09ac\u09b2\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09a5\u09be\u0995\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0 \u09b2\u09be\u09ae\u09bf\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin Y O Z}=\\frac{Q}{\\sin Z O X}=\\frac{R}{\\sin X O Y}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin (\\pi-B O C)}=\\frac{Q}{\\sin (\\pi-A O C)}=\\frac{R}{\\sin (\\pi-O A C)}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin B O C}=\\frac{Q}{\\sin A O C}=\\frac{R}{\\sin O A C}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{P}{\\sin O C A}=\\frac{Q}{\\sin A O C}=\\frac{R}{\\sin O A C}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\frac{P}{O A}=\\frac{Q}{A C}=\\frac{R}{C O} \\quad\\left[\\because \\frac{O A}{\\sin O C A}=\\frac{A C}{\\sin A O C}=\\frac{O C}{\\sin O A C}\\right]<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\angle O A C=90^{\\circ}-B<\/span><\/span><span style=\"font-weight: 400;\">, \u09ac\u09b2\u09c7\u09b0 \u09b8\u09be\u0987\u09a8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{A B}{\\sin O A C}=\\frac{A C}{\\sin O A B}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{A B}{\\sin \\left(90^{\\circ}-B\\right)}=\\frac{A C}{\\sin \\left(90^{\\circ}-C\\right)}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{A B}{\\cos B}=\\frac{A C}{\\cos C} \\quad\u00a0 \\ldots \\ldots (i)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0, \u09a4\u09cd\u09b0\u09bf\u0995\u09cb\u09a3\u09ae\u09bf\u09a4\u09bf\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u0997\u09c1\u09a3\u09be\u09ac\u09b2\u09c0 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{A B}{\\sin C}=\\frac{A C}{\\sin B} \\quad \\ldots\u00a0\\ldots (ii)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">i<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">ii<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ad\u09be\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\sin C}{\\cos \\mathrm{B}}=\\frac{\\sin B}{\\cos C}<\/span><\/span><span style=\"font-weight: 400;\"> \u00a0 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin B \\cos B=\\sin C \\cos C<\/span>\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">2 \\sin B \\cos B=2 \\sin C \\cos C<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin 2 B=\\sin 2 C<\/span>\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"> \u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin 2 B=\\sin \\left(180^{\\circ}-2 C\\right)<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">2 B=180^{\\circ}-2 C<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u092f\u093e, <span class=\"katex-eq\" data-katex-display=\"false\">B=90^{\\circ}-C<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0\u09ac\u09be, <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">B+C=90^{\\circ}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234<\/span> <span style=\"font-weight: 400;\">ABC<\/span><span style=\"font-weight: 400;\"> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u099f\u09bf \u09b8\u09ae\u0995\u09cb\u09a3\u09c0 \u09ac\u09be \u09b8\u09ae\u09a6\u09cd\u09ac\u09bf\u09ac\u09be\u09b9\u09c1\u0964<\/span><\/p>\n<h2><b>\u09b8\u09ae\u09a4\u09b2\u09c0\u09df \u09ac\u09b2\u099c\u09cb\u099f\u09c7\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b6\u09b0\u09cd\u09a4 (Condition of Equilibrium of Coplanar Forces)<\/b><\/h2>\n<p><b>\u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u2013 1 (Theorem &#8211; 1): <\/b><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u099c\u09dc\u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u09aa\u09b0 \u0995\u09be\u09b0\u09cd\u09af\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09ae\u09a4\u09b2\u09c0\u09af\u09bc \u09ac\u09b2 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09b2\u09c7 \u098f\u09b0\u09be \u09b9\u09af\u09bc \u09b8\u09ae\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09ac\u09c7 \u0985\u09a5\u09ac\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf <\/span><span style=\"font-weight: 400;\">P,\u00a0Q,\u00a0R\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u098f\u09a6\u09c7\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09b9\u09af\u09bc \u09b8\u09ae\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09ac\u09c7 \u0985\u09a5\u09ac\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><b>\u09aa\u09cd\u09b0\u09a5\u09ae \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 (In the first case): <\/b><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\">, \u09ac\u09b2\u09c7\u09b0 \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u098f\u09a6\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span><span style=\"font-weight: 400;\">O<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09af\u09bc\u09c7 \u09af\u09be\u09ac\u09c7\u0964 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09b2\u09c7 \u0989\u0995\u09cd\u09a4 \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09ac\u09b2 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09ac\u09b2 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09b0\u09c7\u0996\u09be \u0993 <\/span><span style=\"font-weight: 400;\">P<\/span> <span style=\"font-weight: 400;\">\u0993<\/span> <span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u099b\u09c7\u09a6\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09b9\u09ac\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span><span style=\"font-weight: 400;\">P,\u00a0Q,\u00a0R\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09ae\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-3987 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/23.1-2-1024x637.png\" alt=\"Equilibrium of Coplanar Forces\" width=\"1024\" height=\"637\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.1-2-1024x637.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.1-2-300x187.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.1-2-768x477.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.1-2.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p><b>\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 (In the second case): <\/b><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09c7\u0996\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2\u0964 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u098f\u09a6\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u0993 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09ac\u09c7\u0964 \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u0986\u099b\u09c7 \u0995\u09be\u099c\u09c7\u0987 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09ac\u09b2 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u098f\u0995\u0987 \u09b0\u09c7\u0996\u09be\u09af\u09bc \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 R \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09c7\u0996\u09be <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2 \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-3988 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/23.2-1024x637.png\" alt=\"Equilibrium of Coplanar Forces\" width=\"1024\" height=\"637\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.2-1024x637.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.2-300x187.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.2-768x477.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.2.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">\u2234<\/span><span style=\"font-weight: 400;\"> \u0995\u09cb\u09a8\u09cb \u099c\u09a1\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u09aa\u09b0 \u0995\u09be\u09b0\u09cd\u09af\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09b2\u09c7 \u098f\u09b0\u09be \u09b9\u09af\u09bc \u09b8\u09ae\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09ac\u09c7 \u0985\u09a5\u09ac\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><b>\u0995\u09cb\u09a8\u09cb \u099c\u09a1\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09be\u09b0\u09b8\u09be\u09ae\u09cd\u09af \u09b8\u09ae\u09cd\u09ac\u09b2\u09bf\u09a4 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b6\u09b0\u09cd\u09a4\u09be\u09ac\u09b2\u09c0 \u099b\u09be\u09a1\u09bc\u09be\u0993 \u09a8\u09bf\u09ae\u09cd\u09a8\u09ac\u09b0\u09cd\u09a3\u09bf\u09a4 \u09ac\u09bf\u09b7\u09af\u09bc\u0997\u09c1\u09b2\u09bf \u09ac\u09bf\u09b6\u09c7\u09b7\u09ad\u09be\u09ac\u09c7 \u09b8\u09cd\u09ae\u09b0\u09a3\u09af\u09cb\u0997\u09cd\u09af:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">\u2170<\/span><span style=\"font-weight: 400;\">. \u09b8\u09a0\u09bf\u0995 \u099c\u09cd\u09af\u09be\u09ae\u09bf\u09a4\u09bf\u0995 \u099a\u09bf\u09a4\u09cd\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7 \u0996\u09c1\u09ac\u0987 \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3\u0964 \u0985\u0982\u0995\u09bf\u09a4 \u099a\u09bf\u09a4\u09cd\u09b0\u099f\u09bf\u09b0 \u09ac\u09be\u09b9\u09c1\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af, \u0995\u09cb\u09a3 \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u099c\u09cd\u09af\u09be\u09ae\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c0\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09bf \u09ac\u09bf\u09b6\u09c7\u09b7 \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8\u09c0\u09af\u09bc\u0964 \u09a4\u09cd\u09b0\u09bf\u0995\u09cb\u09a3\u09ae\u09bf\u09a4\u09bf\u0995 <\/span><span style=\"font-weight: 400;\">cot<\/span><span style=\"font-weight: 400;\"> \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09cb\u09a8\u09cb \u0995\u09cb\u09a8\u09cb \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0985\u09aa\u09b0\u09bf\u09b9\u09be\u09b0\u09cd\u09af\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-3989 size-large\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/23.3-1024x645.png\" alt=\"\" width=\"1024\" height=\"645\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.3-1024x645.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.3-300x189.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.3-768x484.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/23.3.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09cd\u09b0\u09bf\u0995\u09cb\u09a3\u09ae\u09bf\u09a4\u09bf\u0995 <\/span><span style=\"font-weight: 400;\">cot<\/span><span style=\"font-weight: 400;\"> \u09b8\u09c2\u09a4\u09cd\u09b0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(a) <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">(m+n) \\cot \\theta=m \\cot \\alpha-n \\cot \\beta<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">(b) <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">(m+n) \\cot \\theta=n \\cot A-m \\cot B<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2171<\/span><span style=\"font-weight: 400;\">.\u00a0<\/span><span style=\"font-weight: 400;\">\u09b8\u09c1\u09b8\u09cd\u09a5\u09bf\u09a4 \u098f\u0995 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ac\u09bf\u09b6\u09c7\u09b7\u09c7 \u09b2\u09be\u09ae\u09bf\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0, \u09ac\u09b2\u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0, \u09ac\u09b2\u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09c3\u09a4 \u09b9\u09af\u09bc\u0964 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09af\u09a6\u09bf \u0985\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u0993 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09c7 \u09a4\u09ac\u09c7 \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09ac\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09a6\u09bf\u0995\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2172<\/span><span style=\"font-weight: 400;\">. \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09c7\u0996\u09be \u09af\u09a6\u09bf \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09a8\u09be \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 \u09b8\u09be\u09ae\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a8\u09bf\u09ae\u09bf\u09a4\u09cd\u09a4\u09c7 \u098f\u09b0\u09be \u0985\u09ac\u09b6\u09cd\u09af\u0987 \u0995\u09cb\u09a8\u09cb \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ae\u09bf\u09b2\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2173<\/span><span style=\"font-weight: 400;\">. \u09b8\u0982\u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u099c\u09a8\u09bf\u09a4 \u09b8\u09c3\u09b7\u09cd\u099f \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0993 \u09aa\u09cd\u09b0\u09a4\u09bf\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09b8\u09ac \u09b8\u09ae\u09af\u09bc \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2174<\/span><span style=\"font-weight: 400;\">. \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09ae\u09b8\u09c3\u09a3 \u09a4\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09a4\u09b2\u09c7\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2175<\/span><span style=\"font-weight: 400;\">. \u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09b0\u09c2\u09aa \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u0993\u099c\u09a8 \u09a6\u09a8\u09cd\u09a1\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7 \u09af\u09be \u0990 \u09a6\u09a8\u09cd\u09a1\u09c7\u09b0 \u09ad\u09be\u09b0\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u0964<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><b>\u099c\u09dc\u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b6\u09c0\u09b2 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/b><b>(<\/b><b>Resultant of Parallel forces acting on a rigid body<\/b><b>)<\/b><\/h2>\n<p><b>\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2<\/b><b>, <\/b><b>\u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u0993 \u0985\u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2 <\/b><b>(<\/b><b>Parallel, like Parallel and Unlike Parallel Forces<\/b><b>)<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09a6\u09c1\u0987 \u09ac\u09be \u09a4\u09a4\u09cb\u09a7\u09bf\u0995 \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09c7\u0996\u09be\u0997\u09c1\u09b2\u09bf \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u09b2\u09c7 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u0995\u09c7 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2 \u09ac\u09b2\u09be \u09b9\u09df\u0964\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u09a6\u09bf\u0995 \u098f\u0995\u0987 \u09b9\u09b2\u09c7 \u09ac\u09b2 \u09a6\u09c1\u0987\u099f\u09bf\u0995\u09c7 \u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u09a6\u09bf\u0995 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09b2\u09c7 \u09ac\u09b2 \u09a6\u09c1\u0987\u099f\u09bf\u0995\u09c7 \u0985\u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/li>\n<\/ul>\n<table>\n<tbody>\n<tr>\n<td><img loading=\"lazy\" class=\"wp-image-3992 aligncenter\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/24.1-4-300x157.png\" alt=\"Parallel force\" width=\"334\" height=\"175\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.1-4-300x157.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.1-4-1024x537.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.1-4-768x403.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.1-4.png 1052w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/td>\n<td><img loading=\"lazy\" class=\"wp-image-3993 aligncenter\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/24.2-2-300x157.png\" alt=\"Parallel forces \" width=\"323\" height=\"169\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.2-2-300x157.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.2-2-1024x537.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.2-2-768x403.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.2-2.png 1052w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 (\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">P,Q,R,S\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">T<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">\u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 (\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2)<\/span><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" class=\"size-medium wp-image-3994 aligncenter\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/24.3-1-300x157.png\" alt=\"Parallel forces \" width=\"300\" height=\"157\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.3-1-300x157.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.3-1-1024x537.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.3-1-768x403.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.3-1.png 1052w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/td>\n<td><img loading=\"lazy\" class=\"size-medium wp-image-3995 aligncenter\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/24.4-1-300x157.png\" alt=\"Parallel forces \" width=\"300\" height=\"157\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.4-1-300x157.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.4-1-1024x537.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.4-1-768x403.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/24.4-1.png 1052w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">\u0985\u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 (\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">Q<\/span><span style=\"font-weight: 400;\"> \u0985\u09b8\u09a6\u09c3\u09b6 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">\u0985\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0 (\u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">P,Q\u00a0<\/span><span style=\"font-weight: 400;\">\u0993 <\/span><span style=\"font-weight: 400;\">R<\/span><span style=\"font-weight: 400;\"> \u09ac\u09b2\u09a4\u09cd\u09b0\u09df \u0985\u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09ac\u09b2\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af (Converse law of triangle law of forces)\u00a0 \u09ac\u09b0\u09cd\u09a3\u09a8\u09be (statement): \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09a5\u09be\u0995\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u098f\u0995\u0987\u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u0995\u09cb\u09a8\u09cb \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7\u0964\u00a0 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/laws-of-force\/\">Read More<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4273,3038,50,3026],"tags":[],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3978"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=3978"}],"version-history":[{"count":15,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3978\/revisions"}],"predecessor-version":[{"id":8388,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3978\/revisions\/8388"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}