{"id":33,"date":"2022-03-24T18:04:24","date_gmt":"2022-03-24T18:04:24","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=33"},"modified":"2023-06-19T15:55:07","modified_gmt":"2023-06-19T09:55:07","slug":"3d-vector-division","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/3d-vector-division\/","title":{"rendered":"\u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09ac\u09bf\u09ad\u09be\u099c\u09a8 (3D Vector Division)"},"content":{"rendered":"\r\n<h2>\u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc (Three-Dimensional Coordinate system) \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09be\u09b6<\/h2>\r\n\r\n\r\n\r\n<p>\u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u0995\u09cb\u09a8\u09cb \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4 \u0989\u09aa\u09be\u09af\u09bc\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09be \u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09ac\u09bf\u09ad\u09be\u099c\u09a8 <strong>(<\/strong><b>Division of 3D rectangular expansion vectors)<\/b> \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09ac\u09bf\u09ac\u09c7\u099a\u09bf\u09a4 \u09b9\u09af\u09bc\u0964<\/p>\r\n\r\n\r\n\r\n<span class=\"katex-eq\" data-katex-display=\"false\">\\overrightarrow{\\mathrm{r}}=\\hat{\\mathrm{i}} \\mathrm{x}+\\hat{\\mathrm{j} \\mathrm{y}}+\\hat{\\mathrm{k} z}<\/span>\r\n\r\n\r\n\r\n<p>\u098f\u0996\u09be\u09a8\u09c7 P-\u098f\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 (x,y,z)\u0964<\/p>\r\n<p>\r\n\r\n<\/p>\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" class=\"aligncenter wp-image-3451\" src=\"https:\/\/stage-wp.10minuteschool.com\/wp-content\/uploads\/2021\/12\/14.1-1-1-1024x730.png\" alt=\"Division of 3D vectors\" width=\"1024\" height=\"730\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-1-1-1024x730.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-1-1-300x214.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-1-1-768x548.png 768w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-1-1.png 1052w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\r\n<\/div>\r\n<p>\r\n\r\n<\/p>\r\n<p>\u09a7\u09b0\u09be \u09af\u09be\u0995, \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u0995\u09cb\u09a3\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 OX, OY \u0993 OZ \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09a4\u09bf\u09a8\u099f\u09bf \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 X, Y \u0993 Z \u0985\u0995\u09cd\u09b7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u099b\u09c7\u0964 OP \u09b0\u09c7\u0996\u09be\u099f\u09bf \u098f\u0987 \u0985\u0995\u09cd\u09b7 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc r \u09ae\u09be\u09a8\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09be\u09b6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u099b\u09c7\u0964<\/p>\r\n<p>\r\n\r\n<\/p>\r\n<p>\u0986\u09b0\u0993 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\overrightarrow{\\mathrm{op}}<\/span> \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09b6\u09c0\u09b0\u09cd\u09b7\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 P-\u098f\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 (x,y,z) \u098f\u09ac\u0982 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 X, Y \u0993 Z \u0985\u0995\u09cd\u09b7\u09c7 \u098f\u0995\u0995 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09be\u09b6\u09bf \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{i},\\hat{j},\\hat{k}<\/span>\u0964 PN \u09b0\u09c7\u0996\u09be\u099f\u09bf \u09b9\u09b2\u09cb XY \u09b8\u09ae\u09a4\u09b2\u09c7\u09b0 \u0989\u09aa\u09b0 \u098f\u09ac\u0982 NQ \u09b0\u09c7\u0996\u09be\u099f\u09bf \u09b9\u09b2\u09cb OX-\u098f\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u0964<\/p>\r\n<p>\r\n\r\n<\/p>\r\n<p>\u099a\u09bf\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09af\u09cb\u0997\u09c7\u09b0 \u09a8\u09bf\u09af\u09bc\u09ae \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09be\u0987,\u00a0<\/p>\r\n<p>\r\n\r\n<\/p>\r\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{c}\n\\overrightarrow{\\mathrm{OP}}=\\overrightarrow{\\mathrm{ON}}+\\overrightarrow{\\mathrm{NP}} \\\\\n\\overrightarrow{\\mathrm{ON}}=\\overrightarrow{\\mathrm{OQ}}+\\overrightarrow{\\mathrm{QN}} \\\\\n\\therefore \\overrightarrow{\\mathrm{OP}}=\\overrightarrow{\\mathrm{OQ}}+\\overrightarrow{\\mathrm{QN}}+\\overrightarrow{\\mathrm{NP}} \\\\\n\\text { \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 } \\overrightarrow{\\mathrm{OQ}}=\\mathrm{xi}, \\overrightarrow{\\mathrm{QN}}=\\mathrm{y} \\hat{\\jmath} \\\\\n\\overrightarrow{\\mathrm{NP}}=\\mathrm{z} \\hat{\\mathrm{k}} \\overrightarrow{\\mathrm{OP}}=\\overrightarrow{\\mathrm{r}} \\\\\n\\therefore \\overrightarrow{\\mathrm{r}}=\\hat{\\mathrm{i}} \\mathrm{x}+\\hat{\\mathrm{j}} \\mathrm{y}+\\hat{\\mathrm{k} z}\n\\end{array}<\/span>\r\n<p>\r\n\r\n<\/p>\r\n<p>\u098f\u0996\u09be\u09a8\u09c7 x,y,z \u00a0\u09b9\u09b2\u09cb \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 X, Y \u0993 Z \u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u0989\u09aa\u09be\u0982\u09b6\u09c7\u09b0 \u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u09b9\u09b2\u09be\u09cb \u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0964<\/p>\r\n<p>\r\n\r\n<\/p>\r\n<h2>\u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09ae\u09be\u09a8 <b>(The value of the vector)<\/b><\/h2>\r\n<p>\r\n\r\n<\/p>\r\n<p><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09be <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span>-\u098f\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u098f\u0995\u0995 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09be\u09b6\u09bf,<\/p>\r\n<p>\r\n\r\n<\/p>\r\n<span class=\"katex-eq\" data-katex-display=\"false\">\\hat{\\mathrm{r}}=\\frac{\\overrightarrow{\\mathrm{r}}}{\\mathrm{r}}=\\frac{\\hat{1} \\mathrm{x}+\\hat{\\jmath} \\mathrm{y}+\\hat{\\mathrm{k} z}}{\\sqrt{\\mathrm{x}^{2}+\\mathrm{y}^{2}+\\mathrm{z}^{2}}}<\/span>\r\n<p>\r\n\r\n<\/p>\r\n<h2><strong>\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 <b>(Radius vector)<\/b><\/strong><\/h2>\r\n<p>\r\n\r\n<\/p>\r\n<p>\u09af\u09c7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09ae\u09c2\u09b2 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc, \u09a4\u09be\u0995\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09ac\u09b2\u09c7\u0964 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0995\u09c7 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 P \u098f\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 (x,y,z) \u09b9\u09b2\u09c7, \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0,<span class=\"katex-eq\" data-katex-display=\"false\">\\overrightarrow{\\mathrm{r}}=\\overrightarrow{\\mathrm{OP}}=\\hat{\\mathrm{i} \\mathrm{X}}+\\hat{\\mathrm{j} \\mathrm{y}}+\\hat{\\mathrm{k} \\mathrm{z}} \\text { \u098f\u09ac\u0982 \u098f\u09b0 \u09ae\u09be\u09a8 } \\mathrm{r}=\\overrightarrow{|\\mathrm{r}|}=\\sqrt{\\mathrm{x}^{2}+\\mathrm{y}^{2}+\\mathrm{z}^{2}}<\/span><\/p>\r\n<p>\r\n\r\n<\/p>\r\n<h2><strong>\u09a6\u09bf\u0995 \u0995\u09cb\u09b8\u09be\u0987\u09a8 (<b>Direction Cosine)<\/b><\/strong><\/h2>\r\n<p>\r\n\r\n<\/p>\r\n<p>\u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u0995\u09be\u09b0\u09cd\u099f\u09c7\u09b8\u09c0\u09af\u09bc \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u098f\u0995\u099f\u09bf \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09a4\u09bf\u09a8\u099f\u09bf \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09af\u09c7 \u09a4\u09bf\u09a8\u099f\u09bf \u0995\u09cb\u09a3 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u0995\u09cb\u09b8\u09be\u0987\u09a8\u09c7\u09b0 (cos) \u098f\u09b0 \u09ae\u09be\u09a8\u0995\u09c7 \u09a6\u09bf\u0995 \u0995\u09cb\u09b8\u09be\u0987\u09a8 \u09ac\u09b2\u09c7\u0964 \u098f\u0995\u099f\u09bf \u09ad\u09c7\u0995\u09cd\u099f\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{A}<\/span>\u00a0 \u09af\u09a6\u09bf \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 X, Y \u0993 Z \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\gamma, \\beta<\/span> \u098f\u09ac\u0982 Y \u0995\u09cb\u09a3 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7 \u09a4\u09be\u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\cos \\alpha, \\cos \\beta<\/span>\u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">\\cos \\gamma<\/span>\u0995\u09c7 \u09a6\u09bf\u0995 \u0995\u09cb\u09b8\u09be\u0987\u09a8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/p>\r\n<p>\r\n\r\n<\/p>\r\n<p>&nbsp;<\/p>\r\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>\u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc (Three-Dimensional Coordinate system) \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u0995\u09cb\u09a8\u09cb \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4 \u0989\u09aa\u09be\u09af\u09bc\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09be \u09a4\u09cd\u09b0\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u09c7\u09b0 \u09ac\u09bf\u09ad\u09be\u099c\u09a8 (Division of 3D rectangular expansion vectors) \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09ac\u09bf\u09ac\u09c7\u099a\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u098f\u0996\u09be\u09a8\u09c7 P-\u098f\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 (x,y,z)\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995, \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/3d-vector-division\/\">Read More<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4236,3028,50,51],"tags":[2409,2410,2412,2411],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/33"}],"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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":10,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/33\/revisions"}],"predecessor-version":[{"id":7007,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/33\/revisions\/7007"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=33"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=33"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}