{"id":2707,"date":"2023-07-21T01:48:22","date_gmt":"2023-07-21T01:48:22","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d0%b2%d0%b8%d1%80%d1%96%d0%b1-%d0%bf%d0%b5%d1%80%d0%b5%d1%82%d0%b8%d0%bd%d0%b0%d1%94-%d0%b2-r\/"},"modified":"2023-07-21T01:48:22","modified_gmt":"2023-07-21T01:48:22","slug":"%d0%b2%d0%b8%d1%80%d1%96%d0%b1-%d0%bf%d0%b5%d1%80%d0%b5%d1%82%d0%b8%d0%bd%d0%b0%d1%94-%d0%b2-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d0%b2%d0%b8%d1%80%d1%96%d0%b1-%d0%bf%d0%b5%d1%80%d0%b5%d1%82%d0%b8%d0%bd%d0%b0%d1%94-%d0%b2-r\/","title":{"rendered":"\u042f\u043a \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0443 r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u041f\u0440\u0438\u043f\u0443\u0441\u043a\u0430\u044e\u0447\u0438, \u0449\u043e \u043c\u0438 \u043c\u0430\u0454\u043c\u043e \u0432\u0435\u043a\u0442\u043e\u0440 A \u0437 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 (A <sub>1<\/sub> , A <sub>2<\/sub> , A <sub>3<\/sub> ) \u0456 \u0432\u0435\u043a\u0442\u043e\u0440 B \u0437 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 (B <sub>1<\/sub> , B <sub>2<\/sub> , B <sub>3<\/sub> ), \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0446\u0438\u0445 \u0434\u0432\u043e\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0456\u0432 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u043c \u0447\u0438\u043d\u043e\u043c:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u041f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a<\/strong> = [(A <sub>2<\/sub> *B <sub>3<\/sub> ) \u2013 (A <sub>3<\/sub> *B <sub>2<\/sub> ), (A <sub>3<\/sub> *B <sub>1<\/sub> ) \u2013 (A <sub>1<\/sub> *B <sub>3<\/sub> ), (A <sub>1<\/sub> *B <sub>2<\/sub> ) \u2013 (A <sub>2<\/sub> *B <sub>1)<\/sub> )]<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u043f\u0440\u0438\u043a\u043b\u0430\u0434, \u043f\u0440\u0438\u043f\u0443\u0441\u0442\u0438\u043c\u043e, \u0449\u043e \u043c\u0438 \u043c\u0430\u0454\u043c\u043e \u0442\u0430\u043a\u0456 \u0432\u0435\u043a\u0442\u043e\u0440\u0438:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0412\u0435\u043a\u0442\u043e\u0440 A: (1, 2, 3)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0412\u0435\u043a\u0442\u043e\u0440 B: (4, 5, 6)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u041c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0446\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0456\u0432 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u043c \u0447\u0438\u043d\u043e\u043c:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u041f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a = [(A <sub>2<\/sub> *B <sub>3<\/sub> ) \u2013 (A <sub>3<\/sub> *B <sub>2<\/sub> ), (A <sub>3<\/sub> *B <sub>1<\/sub> ) \u2013 (A <sub>1<\/sub> *B <sub>3<\/sub> ), (A <sub>1<\/sub> *B <sub>2<\/sub> ) \u2013 (A <sub>2<\/sub> *B <sub>1)<\/sub> )]<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u041f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a = [(2*6) \u2013 (3*5), (3*4) \u2013 (1*6), (1*5) \u2013 (2*4)]<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u041f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a = (-3, 6, -3)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0429\u043e\u0431 \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0434\u0432\u043e\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0456\u0432 \u0443 R, \u043c\u043e\u0436\u043d\u0430 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0442\u0438 \u043e\u0434\u0438\u043d \u0456\u0437 \u0434\u0432\u043e\u0445 \u043c\u0435\u0442\u043e\u0434\u0456\u0432:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0421\u043f\u043e\u0441\u0456\u0431 1: \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0439\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0456\u044e cross() \u043f\u0430\u043a\u0435\u0442\u0430 pracma<\/strong><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">library<\/span> (pracma)\n  \n<span style=\"color: #008080;\">#calculate cross product of vectors A and B\n<\/span>cross(A, B)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u0421\u043f\u043e\u0441\u0456\u0431 2: \u0412\u0438\u0437\u043d\u0430\u0447\u0442\u0435 \u0432\u043b\u0430\u0441\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u044e<\/strong><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define function to calculate cross product<\/span> \ncross &lt;- <span style=\"color: #008000;\">function<\/span> (x, y, i=1:3) {\n  create3D &lt;- <span style=\"color: #008000;\">function<\/span> (x) <span style=\"color: #3366ff;\">head<\/span> (c(x, <span style=\"color: #3366ff;\">rep<\/span> (0, 3)), 3)\n  x &lt;- create3D(x)\n  y &lt;- create3D(y)\n  j &lt;- <span style=\"color: #008000;\">function<\/span> (i) (i-1) <span style=\"color: #800080;\">%%<\/span> 3+1\n  <span style=\"color: #008000;\">return<\/span> (x[j(i+1)]*y[j(i+2)] - x[j(i+2)]*y[j(i+1)])\n}\n\n<span style=\"color: #008080;\">#calculate cross product\n<\/span>cross(A, B)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u0441\u0442\u0443\u043f\u043d\u0456 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0438 \u043f\u043e\u043a\u0430\u0437\u0443\u044e\u0442\u044c, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u043a\u043e\u0436\u0435\u043d \u043c\u0435\u0442\u043e\u0434 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u0446\u0456.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u041f\u0440\u0438\u043a\u043b\u0430\u0434 1. \u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0439\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0456\u044e cross() \u043f\u0430\u043a\u0435\u0442\u0430 pracma<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0439 \u043a\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u0443\u0454, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e <strong>cross()<\/strong> \u0456\u0437 \u043f\u0430\u043a\u0435\u0442\u0430 <a href=\"https:\/\/cran.r-project.org\/web\/packages\/pracma\/index.html\" target=\"_blank\" rel=\"noopener\">pracma<\/a> \u0434\u043b\u044f \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u043e\u0433\u043e \u0434\u043e\u0431\u0443\u0442\u043a\u0443 \u043c\u0456\u0436 \u0434\u0432\u043e\u043c\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (pracma)\n  \n<span style=\"color: #008080;\">#definevectors\n<\/span>A &lt;- c(1, 2, 3)\nB &lt;- c(4, 5, 6)\n  \n<span style=\"color: #008080;\">#calculate cross product\n<\/span>cross(A, B)\n\n[1] -3 6 -3\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u041f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0432\u0438\u044f\u0432\u043b\u044f\u0454\u0442\u044c\u0441\u044f <strong>(-3, 6, -3)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0426\u0435 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0454 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u043e\u043c\u0443 \u0434\u043e\u0431\u0443\u0442\u043a\u0443, \u044f\u043a\u0438\u0439 \u043c\u0438 \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u0432\u0440\u0443\u0447\u043d\u0443 \u0440\u0430\u043d\u0456\u0448\u0435.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u041f\u0440\u0438\u043a\u043b\u0430\u0434 2: \u0412\u0438\u0437\u043d\u0430\u0447\u0442\u0435 \u0432\u043b\u0430\u0441\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u044e<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0423 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u043e\u043c\u0443 \u043a\u043e\u0434\u0456 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u044f\u043a \u0432\u0438\u0437\u043d\u0430\u0447\u0438\u0442\u0438 \u0432\u043b\u0430\u0441\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u044e \u0434\u043b\u044f \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u043e\u0433\u043e \u0434\u043e\u0431\u0443\u0442\u043a\u0443 \u043c\u0456\u0436 \u0434\u0432\u043e\u043c\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define function to calculate cross product<\/span> \ncross &lt;- <span style=\"color: #008000;\">function<\/span> (x, y, i=1:3) {\n  create3D &lt;- <span style=\"color: #008000;\">function<\/span> (x) <span style=\"color: #3366ff;\">head<\/span> (c(x, <span style=\"color: #3366ff;\">rep<\/span> (0, 3)), 3)\n  x &lt;- create3D(x)\n  y &lt;- create3D(y)\n  j &lt;- <span style=\"color: #008000;\">function<\/span> (i) (i-1) <span style=\"color: #800080;\">%%<\/span> 3+1\n  <span style=\"color: #008000;\">return<\/span> (x[j(i+1)]*y[j(i+2)] - x[j(i+2)]*y[j(i+1)])\n}\n\n<span style=\"color: #008080;\">#definevectors\n<\/span>A &lt;- c(1, 2, 3)\nB &lt;- c(4, 5, 6)\n\n<span style=\"color: #008080;\">#calculate cross product\n<\/span>cross(A, B)\n\n[1] -3 6 -3\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u041f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0432\u0438\u044f\u0432\u043b\u044f\u0454\u0442\u044c\u0441\u044f <strong>(-3, 6, -3)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0426\u0435 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0454 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u043e\u043c\u0443 \u0434\u043e\u0431\u0443\u0442\u043a\u0443, \u044f\u043a\u0438\u0439 \u043c\u0438 \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u0432 \u043f\u043e\u043f\u0435\u0440\u0435\u0434\u043d\u044c\u043e\u043c\u0443 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0456.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0414\u043e\u0434\u0430\u0442\u043a\u043e\u0432\u0456 \u0440\u0435\u0441\u0443\u0440\u0441\u0438<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0423 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0445 \u043f\u043e\u0441\u0456\u0431\u043d\u0438\u043a\u0430\u0445 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u044f\u043a \u0432\u0438\u043a\u043e\u043d\u0443\u0432\u0430\u0442\u0438 \u0456\u043d\u0448\u0456 \u0442\u0438\u043f\u043e\u0432\u0456 \u0437\u0430\u0432\u0434\u0430\u043d\u043d\u044f \u0432 R:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/uk\/\u0441\u043a\u0430\u043b\u044f\u0440\u043d\u0438\u0438-\u0434\u043e\u0431\u0443\u0442\u043e\u043a-\u043d\u0430-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0443 R<\/a><br \/> <a href=\"https:\/\/statorials.org\/uk\/\u0442\u043e\u0442\u043e\u0436\u043d\u0430-\u043c\u0430\u0442\u0440\u0438\u0446\u044f-\u0432-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u044e \u0456\u0434\u0435\u043d\u0442\u0438\u0447\u043d\u043e\u0441\u0442\u0456 \u0432 R<\/a><br \/> <a href=\"https:\/\/statorials.org\/uk\/\u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438-\u043f\u043e\u0440\u043e\u0436\u043d\u044e-\u043c\u0430\u0442\u0440\u0438\u0446\u044e-\u0432-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u043f\u043e\u0440\u043e\u0436\u043d\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u044e \u0432 R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041f\u0440\u0438\u043f\u0443\u0441\u043a\u0430\u044e\u0447\u0438, \u0449\u043e \u043c\u0438 \u043c\u0430\u0454\u043c\u043e \u0432\u0435\u043a\u0442\u043e\u0440 A \u0437 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 (A 1 , A 2 , A 3 ) \u0456 \u0432\u0435\u043a\u0442\u043e\u0440 B \u0437 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 (B 1 , B 2 , B 3 ), \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a \u0446\u0438\u0445 \u0434\u0432\u043e\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0456\u0432 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u043c \u0447\u0438\u043d\u043e\u043c: \u041f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0438\u0439 \u0434\u043e\u0431\u0443\u0442\u043e\u043a = [(A 2 *B 3 ) \u2013 (A 3 *B 2 ), 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