{"id":3807,"date":"2021-01-30T12:27:46","date_gmt":"2021-01-30T12:27:46","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3807"},"modified":"2023-06-22T17:08:20","modified_gmt":"2023-06-22T11:08:20","slug":"laws-of-forces","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/laws-of-forces\/","title":{"rendered":"\u09ac\u09b2 \u09b8\u0982\u09af\u09cb\u099c\u09a8, \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 \u0993 \u09ac\u09b2\u099c\u09cb\u099f\u09c7\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be"},"content":{"rendered":"

\u09ac\u09b2 \u09b8\u0982\u09af\u09cb\u099c\u09a8\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09b8\u09c2\u09a4\u09cd\u09b0 (Triangle law of forces of composition)<\/b> \u00a0<\/b><\/h2>\n

\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (Statement): <\/b>\u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u0995\u0987 \u09b8\u09ae\u09af\u09bc\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \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 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09b2\u09c7, \u09ac\u09b2 \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u099f\u09bf\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (Proof): <\/b>\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2 <\/span>P<\/span> \u0993 <\/span>Q<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>OAB<\/span> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 <\/span>OA<\/span> \u0993 <\/span>AB<\/span> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4\u0964 <\/span>OB<\/span> \u0995\u09c7 \u0995\u09b0\u09cd\u09a3 \u09a7\u09b0\u09c7, <\/span>OABC<\/span> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09bf\u0964<\/span><\/p>\n

\"\u09ac\u09b2<\/p>\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1, <\/span>AB\u2225OC<\/span>, \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>OC<\/span> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09ac\u09b2\u099f\u09bf\u0993 <\/span>Q<\/span> \u09b9\u09ac\u09c7\u0964 \u098f\u0996\u09a8 \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 <\/span>OA<\/span> \u0993 <\/span>OC<\/span> \u09ac\u09be\u09b9\u09c1 \u09a6\u09c1\u0987\u099f\u09bf \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995\u09c7\u09b0 \u0995\u09b0\u09cd\u09a3 <\/span>OB<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09aa\u09be\u0987, <\/span>\\overrightarrow{O A}+\\overrightarrow{O C}=\\overrightarrow{O B}<\/span><\/span>\u00a0 <\/span>\u09ac\u09be<\/span>, <\/span>\\overrightarrow{O A}+\\overrightarrow{A B}=\\overrightarrow{O B}<\/span><\/span><\/p>\n

\u09ac\u09b2 \u09b8\u0982\u09af\u09cb\u099c\u09a8\u09c7\u09b0 \u09ac\u09b9\u09c1\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0 (Polygon law of forces of composition)<\/b>\u00a0<\/b><\/h2>\n

\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (Statement):<\/b> \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u0995\u0987 \u09b8\u09ae\u09af\u09bc\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 <\/span>(n-1)<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u0995\u09cb\u09a8\u09cb <\/span>n<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09ac\u09be\u09b9\u09c1\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09ac\u09b9\u09c1\u09ad\u09c1\u099c\u09c7\u09b0 \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 <\/span>(n-1)<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09b2\u09c7, \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u0990 \u09ac\u09b9\u09c1\u09ad\u09c1\u099c\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u0985\u09ac\u09b6\u09bf\u09b7\u09cd\u099f <\/span>n<\/span> \u09a4\u09ae \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (Proof): <\/b>\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2 \u09aa\u09be\u0981\u099a\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>OABCDE<\/span> \u09b7\u09dc\u09ad\u09c1\u099c\u09c7\u09b0 \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 <\/span>OA,\u00a0AB,\u00a0BC,\u00a0CD,\u00a0DE\u00a0<\/span>\u09ac\u09be\u09b9\u09c1\u0997\u09c1\u09b2\u09bf \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4\u0964<\/span><\/p>\n

\"Polygon<\/p>\n

\u098f\u0996\u09a8 \u09ac\u09b2 \u09b8\u0982\u09af\u09cb\u099c\u09a8\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span>\\triangle O A B<\/span><\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987, <\/span>\\overrightarrow{O A}+\\overrightarrow{A B}=\\overrightarrow{O B} \\ldots \\ldots<\/span><\/span> (<\/span>i<\/span>)<\/span><\/p>\n

\u098f\u09ac\u0982 <\/span>\\triangle O B C<\/span><\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987, <\/span>\\overrightarrow{O B}+\\overrightarrow{B C}=\\overrightarrow{O C} \\ldots \\ldots<\/span><\/span> (<\/span>ii<\/span>)<\/span><\/p>\n

(<\/span>i<\/span>)<\/span>\u00a0<\/span>\u0993 <\/span>(<\/span>ii<\/span>)<\/span> \u09b9\u09a4\u09c7 \u09aa\u09be\u0987, <\/span>\\overrightarrow{O A}+\\overrightarrow{A B}=\\overrightarrow{O C}-\\overrightarrow{B C}<\/span><\/span> \u09ac\u09be, <\/span>\\overrightarrow{O A}+\\overrightarrow{A B}+\\overrightarrow{B C}=\\overrightarrow{O C}<\/span><\/span><\/p>\n

\u098f\u0995\u0987\u09ad\u09be\u09ac\u09c7 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09b2\u09c7\u0987 \u09aa\u09be\u0987, <\/span>\\overrightarrow{O A}+\\overrightarrow{A B}+\\overrightarrow{B C}+\\overrightarrow{C D}+\\overrightarrow{D E}=\\overrightarrow{O E}<\/span><\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b7\u09dc\u09ad\u09c1\u099c\u09c7\u09b0 \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u09aa\u09be\u0981\u099a\u099f\u09bf \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09b2\u09c7, \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09b7\u09dc\u09ad\u09c1\u099c\u099f\u09bf\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u0995\u09cd\u09b0\u09ae\u09c7 \u0997\u09c3\u09b9\u09c0\u09a4 \u0985\u09ac\u09b6\u09bf\u09b7\u09cd\u099f \u09b7\u09b7\u09cd\u09a0\u09a4\u09ae \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09df\u0964<\/p>\n

\u0995\u09be\u099c:<\/b> \u098f\u0995 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 <\/span>P<\/span> \u0993 <\/span>Q<\/span> \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2, \u098f\u09a6\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R<\/span> \u09ac\u09b2\u09c7\u09b0 \u0989\u09ad\u09af\u09bc \u09a6\u09bf\u0995\u09c7 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 <\/span>30^{\\circ}<\/span><\/span> \u0993 <\/span>60^{\\circ}<\/span><\/span> \u0995\u09cb\u09a3\u09c7 \u0986\u09a8\u09a4\u0964 \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u0964<\/span><\/p>\n

\u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 (Resolved parts of forces)<\/b><\/h2>\n

\u0995\u09cb\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09b2 \u09ac\u09b2\u09a4\u09c7 \u09af\u09a6\u09bf \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c1\u099f\u09bf \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2 \u09a6\u09c1\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u0985\u0982\u09b6\u09c7 \u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 \u0985\u0982\u09b6 \u09a6\u09c1\u099f\u09bf\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0990 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u0964\u00a0<\/span><\/p>\n

\"\u09ac\u09b2<\/p>\n

\"Resolved<\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>OX<\/span> \u0993 <\/span>OY<\/span> \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09a6\u09c1\u0987\u099f\u09bf \u09b2\u09ae\u09cd\u09ac \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u098f\u09ac\u0982 <\/span>OX<\/span> \u098f\u09b0 \u09b8\u09be\u09a5\u09c7 <\/span> \\alpha<\/span> \u0995\u09cb\u09a3\u09c7 \u0986\u09a8\u09a4 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be <\/span>OC<\/span>, \u09af\u09be \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09b2 <\/span>F-<\/span> \u0995\u09c7 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09c7\u0964 \u098f\u0996\u09be\u09a8\u09c7 <\/span>OX<\/span> \u09ac\u09be <\/span>OX<\/span>‘<\/span> \u09b9\u09b2 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09b0\u09c7\u0996\u09be \u098f\u09ac\u0982 <\/span>OY<\/span> \u09b9\u09b2 \u0989\u09b2\u09ae\u09cd\u09ac \u09b0\u09c7\u0996\u09be\u0964 <\/span>C<\/span> \u09a5\u09c7\u0995\u09c7 <\/span>OX<\/span> (\u09ac\u09be <\/span>OX<\/span>‘<\/span>) \u098f\u09b0 \u0989\u09aa\u09b0 <\/span>CA<\/span> \u098f\u09ac\u0982 <\/span>OY<\/span> \u098f\u09b0 \u0989\u09aa\u09b0 <\/span>CB<\/span> \u09b2\u09ae\u09cd\u09ac \u0986\u0981\u0995\u09bf\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span>OACB<\/span> \u098f\u0995\u099f\u09bf \u0986\u09af\u09bc\u09a4\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u09b9\u09af\u09bc\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \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 <\/span>F<\/span> \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09a6\u09cd\u09ac\u09af\u09bc \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>OA<\/span> \u098f\u09ac\u0982 <\/span>OB<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09e7\u09ae \u099a\u09bf\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span>\\cos C O A=\\frac{O A}{O C}<\/span><\/span><\/p>\n

\u09ac\u09be, <\/span>O A=O C \\cos \\alpha=F \\cos \\alpha<\/span><\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 X- \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \\alpha<\/span>\u00a0<\/span> \u0995\u09cb\u09a3\u09c7 \u0986\u09a8\u09a4 \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09a6\u09cd\u09ac\u09af\u09bc \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>F \\cos \\alpha<\/span><\/span> \u0993 <\/span>F \\sin \\alpha^{\\prime}<\/span><\/span><\/p>\n

\u09e8\u09df \u099a\u09bf\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span>\\cos C O A=\\frac{O A}{O C}<\/span><\/span><\/p>\n

\u09ac\u09be, <\/span>O A=O C \\cos \\left(180^{\\circ}-\\alpha\\right)=-F \\cos \\alpha<\/span><\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>X<\/span>‘<\/span>– \u0985\u0995\u09cd\u09b7\u09c7\u09b0 (X-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09a6\u09bf\u0995) \u09b8\u09be\u09a5\u09c7 <\/span>180^{\\circ}-\\alpha<\/span><\/span> \u0995\u09cb\u09a3\u09c7 \u0986\u09a8\u09a4 \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09a6\u09cd\u09ac\u09af\u09bc \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>-F \\cos \\alpha<\/span><\/span> \u0993 <\/span>F \\sin \\alpha<\/span><\/span><\/p>\n

\u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af (Theorem on Resolved parts)<\/b><\/h2>\n

\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (Statement):<\/b> \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u0990 \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u098f\u0995\u0987 \u09a6\u09bf\u0995\u09c7 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n

\"Theorem<\/p>\n

\"Theorem<\/p>\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (Proof): <\/b>\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 <\/span>P<\/span> \u0993 <\/span>Q<\/span> \u09ac\u09b2 \u09a6\u09c1\u0987\u099f\u09bf \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>OA<\/span> \u098f\u09ac\u0982 <\/span>OB<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span>OACB<\/span> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995\u09c7\u09b0 \u0995\u09b0\u09cd\u09a3 <\/span>OC<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0989\u0995\u09cd\u09a4 \u09ac\u09b2\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R<\/span> \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09a7\u09b0\u09bf, <\/span>OX<\/span> \u09b0\u09c7\u0996\u09be\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7, \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>OX<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

A<\/span>, <\/span>B<\/span> \u0993 <\/span>C<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a5\u09c7\u0995\u09c7 <\/span>OX<\/span> \u09ac\u09be <\/span>OX’\u00a0<\/span>(\u09e8\u09af\u09bc \u099a\u09bf\u09a4\u09cd\u09b0\u09c7) \u098f\u09b0 \u0993\u09aa\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>AL,\u00a0BM\u00a0<\/span>\u0993 <\/span>CN<\/span> \u09b2\u09ae\u09cd\u09ac \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09bf\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span>OX<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 <\/span>P,\u00a0Q\u00a0<\/span>\u098f\u09ac\u0982 <\/span>R<\/span> \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>OL,\u00a0OM\u00a0<\/span>\u098f\u09ac\u0982 <\/span>ON<\/span> \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, <\/span>OL + OM = ON<\/span><\/p>\n

\u098f\u0996\u09a8 <\/span>A<\/span> \u09b9\u09a4\u09c7 <\/span>CN<\/span> \u098f\u09b0 \u0989\u09aa\u09b0 <\/span>AE<\/span> \u09b2\u09ae\u09cd\u09ac \u09b8\u0982\u0995\u09a8 \u0995\u09b0\u09bf\u0964<\/span><\/p>\n

\\triangle A C E<\/span> <\/span>\u0993<\/span> \\triangle O B M<\/span><\/span> \u09b8\u09b0\u09cd\u09ac\u09b8\u09ae\u0964 \u0995\u09be\u09b0\u09a3 <\/span>\\triangle A C E<\/span> <\/span>\u0993<\/span> \\triangle O B M<\/span><\/span> \u09b8\u09ae\u0995\u09cb\u09a3\u09c0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7\u00a0<\/span>AC = OB\u00a0<\/span>\u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ac\u09be\u09b9\u09c1 \u09ac\u09b2\u09c7, \u0985\u09a8\u09c1\u09b0\u09c2\u09aa \u0995\u09cb\u09a3 <\/span>\\angle B O M=\\angle C A E . \\quad \\therefore O M=A E=L N<\/span><\/span><\/p>\n

\u09e7\u09ae \u099a\u09bf\u09a4\u09cd\u09b0\u09c7, <\/span>OX<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09b8\u0995\u09b2 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u0997\u09c1\u09b2\u09bf\u0987 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09e8\u09af\u09bc \u099a\u09bf\u09a4\u09cd\u09b0\u09c7, <\/span>Q<\/span> \u098f\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09af\u09be <\/span>\u2018-<\/span>OM\u2019\u00a0<\/span>\u098f\u09b0 \u09b8\u09ae\u09be\u09a8\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09e7\u09ae \u099a\u09bf\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span>OX<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 <\/span>P<\/span> \u0993 <\/span>Q<\/span> \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf <\/span>=O L+O M=O L+L N=O N<\/span>,<\/span>\u00a0\u09af\u09be, <\/span>OX<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf R \u098f\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u0964<\/span><\/p>\n

\u09e8\u09df \u099a\u09bf\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span>OX<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 <\/span>P<\/span> \u0993 <\/span>Q<\/span> \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf <\/span>=O L-O M=O L-L N=O N<\/span>, \u09af\u09be <\/span>OX<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R<\/span> \u098f\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u0964\u00a0<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u0990 \u098f\u0995\u0987 \u09a6\u09bf\u0995\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n

\u09a6\u09cd\u09b0\u09b7\u09cd\u099f\u09ac\u09cd\u09af (Note):<\/b> (<\/span>i<\/span>)<\/span> \u09af\u09a6\u09bf <\/span>P,\u00a0Q\u00a0<\/span>\u0993 \u09a4\u09be\u09a6\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R,\u00a0OX\u00a0<\/span>\u098f\u09b0 \u09b8\u09be\u09a5\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \\alpha<\/span><\/span>, \\beta<\/span><\/span> \u0993 <\/span> \\theta<\/span> \u0995\u09cb\u09a3 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7 \u09a4\u09ac\u09c7 \u0989\u09aa\u09b0\u09cb\u0995\u09cd\u09a4 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span>P \\cos \\alpha+Q \\cos \\beta=R \\cos \\theta<\/span><\/span> \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

(<\/span>ii<\/span>)<\/span> \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a6\u09c1\u0987 \u098f\u09b0 \u0985\u09a7\u09bf\u0995 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u098f\u0995\u09a4\u09b2\u09c0\u09df \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u0993 \u098f\u0987 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af\u099f\u09bf \u09b8\u09a4\u09cd\u09af\u0964\u00a0<\/span><\/p>\n

\u09ac\u09bf\u09b6\u09c7\u09b7 \u09a6\u09cd\u09b0\u09b7\u09cd\u099f\u09ac\u09cd\u09af (Special Note): <\/b>P<\/span> \u0993 <\/span>Q<\/span> \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u00a0 <\/span>R,\u00a0P\u00a0<\/span>\u09ac\u09b2\u09c7\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u09b9\u09b2\u09c7, <\/span>R=\\sqrt{Q^{2}-P^{2}}<\/span><\/span> \u098f\u09ac\u0982 \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cb\u09a3 <\/span>\\cos ^{-1}\\left(\\frac{-P}{Q}\\right)<\/span><\/span> ; \u09af\u09c7\u0996\u09be\u09a8\u09c7 <\/span>P<Q<\/span><\/span><\/p>\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (Proof):<\/b>\u00a0<\/b><\/p>\n

\"Theorem<\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>P<\/span> \u0993 <\/span>Q<\/span> \u09ac\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cb\u09a3 \\alpha<\/span><\/span> \u0964 <\/span>P<\/span> \u0993 <\/span>R<\/span> \u098f\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cb\u09a3 <\/span>90^{\\circ}<\/span><\/span>\u0964<\/span><\/p>\n

P<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,\u00a0\u00a0<\/span><\/p>\n

P \\cos 0^{\\circ}+Q \\cos \\alpha=R \\cos 90^{0}<\/span> <\/span>\u09ac\u09be<\/span>, P+Q \\cos \\alpha=0<\/span> <\/span>\u09ac\u09be<\/span>, \\cos \\alpha=-\\frac{P}{Q} \\therefore \\alpha=\\cos ^{-1}\\left(-\\frac{P}{Q}\\right)<\/span><\/span><\/p>\n

\u098f\u09ac\u0982 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R=\\sqrt{P^{2}+Q^{2}+2 P Q \\cos \\alpha}=\\sqrt{P^{2}+Q^{2}+2 P(-P)}<\/span><\/span><\/p>\n

=\\sqrt{P^{2}+Q^{2}-2 P^{2}=} \\sqrt{Q^{2}-P^{2}}<\/span><\/span><\/p>\n

\u09ac\u09b2\u099c\u09cb\u099f\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf (Resultant of a system of forces)<\/b><\/h2>\n

\u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09b8\u09ae\u09a4\u09b2\u09c0\u09df \u09ac\u09b2\u099c\u09cb\u099f\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09df<\/b>\u00a0<\/b><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>O<\/span> \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u098f\u09ac\u0982 <\/span>OX<\/span> \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09b0\u09c7\u0996\u09be\u0964 \u098f\u0996\u09a8 <\/span>O X \\perp O Y<\/span><\/span> \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09bf\u0964<\/span><\/p>\n

\u09a7\u09b0\u09bf, <\/span>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 <\/span>P_{1}, P_{2}, P_{3}, \\ldots \\ldots<\/span><\/span> \u09b8\u09ae\u09a4\u09b2\u09c0\u09af\u09bc \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>\\mathrm{OA}_{1}, \\mathrm{OA}_{2}, \\mathrm{OA}_{3}, \\ldots \\ldots \\ldots<\/span><\/span> \u09b0\u09c7\u0996\u09be \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u098f\u09ac\u0982 <\/span>OX<\/span> \u098f\u09b0 \u09b8\u09be\u09a5\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>\\alpha_{1}, \\alpha_{2}, \\alpha_{3}, \\ldots \\ldots<\/span><\/span> \u0995\u09cb\u09a3 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7\u0964\u00a0<\/span><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R,\u00a0OA\u00a0<\/span>\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u098f\u09ac\u0982 <\/span>OX<\/span> \u098f\u09b0 \u09b8\u09be\u09a5\u09c7 <\/span> \\theta<\/span> \u0995\u09cb\u09a3 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u0995\u09cb\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7 \u0995\u09cb\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u09af\u09c7 \u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u098f\u0995\u09a4\u09b2\u09c0\u09af\u09bc \u09ac\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 \u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u0990 \u098f\u0995\u0987 \u09a6\u09bf\u0995\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964 \u0985\u09a4\u098f\u09ac <\/span>OX\u00a0<\/span>\u0993 <\/span>OY<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6 \u09a8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n

R \\cos \\theta=P_{1} \\cos \\alpha_{1}+P_{2} \\cos \\alpha_{2}+P_{3} \\cos \\alpha_{3}+\\ldots \\ldots \\ldots=X<\/span><\/span>\u00a0 (\u09a7\u09b0\u09bf)<\/span><\/p>\n

R \\sin \\theta=P_{1} \\sin \\alpha_{1}+P_{2} \\sin \\alpha_{2}+P_{3} \\sin \\alpha_{3}+\\ldots \\ldots \\ldots=Y<\/span><\/span>\u00a0 (\u09a7\u09b0\u09bf)<\/span><\/p>\n

\"Resultant<\/p>\n

\u09a4\u09be\u09b9\u09b2\u09c7, <\/span>X^{2}+Y^{2}=R^{2}\\left(\\cos ^{2} \\theta+\\sin ^{2} \\theta\\right)<\/span><\/span>\u00a0 [\u09ac\u09b0\u09cd\u0997 \u0995\u09b0\u09be\u09b0 \u09aa\u09b0 \u09af\u09cb\u0997 \u0995\u09b0\u09c7]<\/span><\/p>\n

\u09ac\u09be, <\/span>R=\\sqrt{X^{2}+Y^{2}}<\/span><\/span>\u00a0 \u098f\u09ac\u0982 <\/span>\\frac{Y}{X}=\\tan \\theta<\/span><\/span> \u00a0 [\u09ad\u09be\u0997 \u0995\u09b0\u09c7]<\/span><\/p>\n

\u09ac\u09be, <\/span>\\theta=\\tan ^{-1} \\frac{Y}{X}<\/span><\/span>\u00a0
\n<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 <\/span>R=\\sqrt{X^{2}+Y^{2}}<\/span><\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u098f\u09ac\u0982 <\/span>\\theta=\\tan ^{-1} \\frac{Y}{X}<\/span><\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09a6\u09bf\u0995 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n

\u09ac\u09b2\u099c\u09cb\u099f\u09c7\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be (Equilibrium of a system of forces) <\/b>\u00a0<\/b><\/h2>\n

\u09af\u0996\u09a8 \u09a6\u09c1\u0987 \u09ac\u09be \u09a4\u09a4\u09cb\u09a7\u09bf\u0995 \u09ac\u09b2 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u0995\u09be\u09b0\u09cd\u09af\u09b0\u09a4 \u09b9\u09af\u09bc\u09c7 \u098f\u0995\u09c7 \u0985\u09aa\u09b0\u0995\u09c7 \u09a8\u09bf\u09b7\u09cd\u0995\u09cd\u09b0\u09bf\u09af\u09bc \u0995\u09b0\u09c7 \u098f\u09ac\u0982 \u09af\u09be\u09b0 \u09ab\u09b2\u09c7 \u0990 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc \u098f\u09ae\u09a4\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u0995\u09cb\u09a8\u09cb \u0997\u09a4\u09bf\u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09b9\u09ac\u09c7 \u09a8\u09be\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u09aa\u09c2\u09b0\u09cd\u09ac\u09c7\u09b0 \u09a8\u09cd\u09af\u09be\u09af\u09bc \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09ac\u09c7\u0964 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u0995\u09c7 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be \u09ac\u09b2\u09c7\u0964 \u098f\u099f\u09bf \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u0995\u09b0\u09be \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8 \u09af\u09c7, \u09af\u09a6\u09bf \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u098f\u0995\u099f\u09bf \u09ac\u09b2 \u0985\u09ac\u09b6\u09bf\u09b7\u09cd\u099f \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u098f\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09ac\u09c7\u0964 \u0995\u09be\u099c\u09c7\u0987 \u09b8\u09ae\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09ac\u09b2\u09c7\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09ae\u09c2\u09b2\u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09b2\u09cb \u201c\u09b8\u09c1\u09b8\u09cd\u09a5\u09bf\u09a4 \u09ac\u09b2\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af\u201d\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0995\u09bf\u099b\u09c1\u09b8\u0982\u0996\u09cd\u09af\u0995 \u09b8\u09ae\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09ac\u09b2 \u09b8\u09cd\u09a5\u09bf\u09a4\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09b2\u09c7 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09a6\u09bf\u0995\u09c7 \u098f\u09a6\u09c7\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09bf\u09b7\u09cd\u099f\u09be\u0982\u09b6\u09c7\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u0989\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \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<\/b><\/p>\n

(Condition of equilibrium of a system of coplanar forces acting on a particle)<\/b><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>P_{1}, P_{2}, P_{3}, \\ldots \\ldots \\ldots<\/span><\/span> \u0995\u09a4\u0995\u0997\u09c1\u09b2\u09bf \u09b8\u09ae\u09a4\u09b2\u09c0\u09af\u09bc \u09ac\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f <\/span>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be \u0995\u09b0\u09c7\u0964 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R<\/span> \u098f\u09ac\u0982 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u09bf\u0995 <\/span>OX<\/span> \u0993 <\/span>OY<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>X<\/span> \u0993 <\/span>Y<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09b2\u09c7, <\/span>R=\\sqrt{X^{2}+Y^{2}}<\/span><\/span><\/p>\n

\"equilibrium<\/p>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>R=0<\/span><\/span> \u09ac\u09be, <\/span>X^{2}+Y^{2}=0<\/span><\/span> \u09b9\u09ac\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 <\/span>X<\/span> \u0993 <\/span>Y<\/span> \u098f\u09b0 \u0989\u09ad\u09af\u09bc\u09c7\u0987 \u09b6\u09c2\u09a8\u09cd\u09af <\/span>(<\/span>0)\u00a0<\/span>\u09a8\u09be \u09b9\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>X\u00a0=\u00a00,\u00a0Y\u00a0=\u00a00<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac \u09b8\u09ae\u09a4\u09b2\u09c0\u09af\u09bc \u09ac\u09b2\u099c\u09cb\u099f \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09be\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8\u09c0\u09af\u09bc \u09b6\u09b0\u09cd\u09a4 (necessary condition) \u09b9\u09b2 \u09b2\u09ae\u09cd\u09ac\u09b0\u09c7\u0996\u09be <\/span>OX<\/span> \u0993 <\/span>OY<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09a4\u09be\u09a6\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09be\u0982\u09b6\u09c7\u09b0 <\/span>\u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09aa\u09c3\u09a5\u0995 \u09aa\u09c3\u09a5\u0995\u09ad\u09be\u09ac\u09c7 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>X\u00a0=\u00a00,\u00a0Y\u00a0=\u00a00\u00a0<\/span>\u09b9\u09b2\u09c7 <\/span>R=\\sqrt{X^{2}+Y^{2}}<\/span><\/span> \u09b9\u09ac\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \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\u09ac\u09c7\u0964 \u098f\u0987 \u09b6\u09b0\u09cd\u09a4 \u09b9\u09b2 \u09ac\u09b2\u099c\u09cb\u099f\u09c7\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09be\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09aa\u09cd\u09a4 (Sufficient condition) \u09b6\u09b0\u09cd\u09a4\u0964<\/span><\/p>\n

\u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09ac\u09b2\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c \u09b8\u09c2\u09a4\u09cd\u09b0 (Triangle Law of Force in Equilibrium)<\/b><\/h2>\n

\u09ac\u09b0\u09cd\u09a3\u09a8\u09be (statement): <\/b>\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09af\u09a6\u09bf \u098f\u0995\u099f\u09bf \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09df \u09a4\u09ac\u09c7 \u09ac\u09b2\u0997\u09c1\u09b2\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09a5\u09be\u0995\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 (Proof): <\/b>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 <\/span>P,\u00a0Q\u00a0<\/span>\u0993 <\/span>R\u00a0<\/span>\u098f\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>ABC<\/span> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 <\/span>BC,\u00a0CA\u00a0\u00a0AB<\/span> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4\u0964 \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\u09df \u09a5\u09be\u0995\u09ac\u09c7\u0964<\/span><\/p>\n

\"Triangle<\/p>\n

\"Triangle<\/p>\n

BC\u2225AD<\/span> \u098f\u09ac\u0982 <\/span>CA\u2225BD<\/span> \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09c7 <\/span>BCAD<\/span> \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u0997\u09a0\u09a8 \u0995\u09b0\u09bf\u0964 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc <\/span>CA<\/span> \u0993 <\/span>BD<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u098f\u0995\u0987 \u09ac\u09b2 <\/span>Q<\/span> \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964\u00a0\u00a0<\/span><\/p>\n

\u098f\u0996\u09a8 \u09ac\u09b2\u09c7\u09b0 \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995 \u09b8\u09c1\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <\/span>BC<\/span> \u0993 <\/span>BD<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 <\/span>P<\/span> \u0993 <\/span>Q<\/span> \u098f\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf <\/span>R,\u00a0BA\u00a0<\/span>\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u098f\u09ac\u0982 <\/span>B<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09b9\u09ac\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u098f\u0987 \u09ac\u09b2\u099f\u09bf <\/span>AB<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 <\/span>R<\/span> \u09ac\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09b9\u09ac\u09c7 \u098f\u09ac\u0982 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09a8\u09bf\u09b7\u09cd\u0995\u09cd\u09b0\u09bf\u09df \u0995\u09b0\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

\u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf (Vector method): <\/b>\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b0\u09a4 \u09a4\u09bf\u09a8\u099f\u09bf \u09ac\u09b2 <\/span>P,\u00a0Q\u00a0<\/span>\u0993 <\/span>R<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 ABC \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 <\/span>BC,\u00a0CA\u00a0<\/span>\u0993 <\/span>AB<\/span> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09df\u0964\u00a0<\/span><\/p>\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, \u09ac\u09b2 \u09a4\u09bf\u09a8\u099f\u09bf\u09b0 \u09b8\u09be\u09ae\u09cd\u09af\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>P+Q+R=0<\/span><\/span><\/p>\n

BCAD \u09b8\u09be\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u0995\u099f\u09bf \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u0995\u09b0\u09bf\u0964 <\/span>CA<\/span> \u0993 <\/span>BD<\/span> \u09ac\u09be\u09b9\u09c1\u09a6\u09cd\u09ac\u09df \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09ac\u09b2\u09c7, <\/span>BD<\/span> \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be <\/span>Q<\/span> \u09ac\u09b2\u0995\u09c7 \u09ae\u09be\u09a8\u09c7 \u0993 \u09a6\u09bf\u0995\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09be \u09af\u09be\u09df\u0964\u00a0<\/span><\/p>\n

\u098f\u0996\u09a8, <\/span>P+Q+R=\\overrightarrow{B C}+\\overrightarrow{C A}+\\overrightarrow{A B}=\\overrightarrow{B C}+\\overrightarrow{B D}+\\overrightarrow{A B}=\\overrightarrow{B A}+\\overrightarrow{A B}=0<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u09ac\u09b2 \u09b8\u0982\u09af\u09cb\u099c\u09a8\u09c7\u09b0 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09b8\u09c2\u09a4\u09cd\u09b0 (Triangle law of forces of composition) \u00a0 \u09ac\u09b0\u09cd\u09a3\u09a8\u09be (Statement): \u098f\u0995\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u0995\u0987 \u09b8\u09ae\u09af\u09bc\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09a4 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \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 \u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09be\u09b9\u09c1 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u09b9\u09b2\u09c7, \u09ac\u09b2 \u09a6\u09c1\u0987\u099f\u09bf\u09b0 \u09b2\u09ac\u09cd\u09a7\u09bf\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u099f\u09bf\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4<\/p>\n

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":[4273,3038,3026],"tags":[],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3807"}],"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=3807"}],"version-history":[{"count":17,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3807\/revisions"}],"predecessor-version":[{"id":8362,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3807\/revisions\/8362"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3807"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3807"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}