{"id":2710,"date":"2023-07-21T01:48:22","date_gmt":"2023-07-21T01:48:22","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%91%e1%80%af%e1%80%90%e1%80%ba%e1%80%80%e1%80%af%e1%80%94%e1%80%ba%e1%80%9e%e1%80%8a%e1%80%ba-r-%e1%80%96%e1%80%bc%e1%80%84%e1%80%b7%e1%80%ba%e1%80%96%e1%80%bc%e1%80%90%e1%80%ba%e1%80%9e\/"},"modified":"2023-07-21T01:48:22","modified_gmt":"2023-07-21T01:48:22","slug":"%e1%80%91%e1%80%af%e1%80%90%e1%80%ba%e1%80%80%e1%80%af%e1%80%94%e1%80%ba%e1%80%9e%e1%80%8a%e1%80%ba-r-%e1%80%96%e1%80%bc%e1%80%84%e1%80%b7%e1%80%ba%e1%80%96%e1%80%bc%e1%80%90%e1%80%ba%e1%80%9e","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%91%e1%80%af%e1%80%90%e1%80%ba%e1%80%80%e1%80%af%e1%80%94%e1%80%ba%e1%80%9e%e1%80%8a%e1%80%ba-r-%e1%80%96%e1%80%bc%e1%80%84%e1%80%b7%e1%80%ba%e1%80%96%e1%80%bc%e1%80%90%e1%80%ba%e1%80%9e\/","title":{"rendered":"R \u1016\u103c\u1004\u1037\u103a cross product \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a vector A \u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1012\u103c\u1015\u103a\u1005\u1004\u103a\u1019\u103b\u102c\u1038 (A <sub>1<\/sub> \u104a A <sub>2<\/sub> \u104a A <sub>3<\/sub> ) \u1014\u103e\u1004\u1037\u103a vector B \u1019\u103b\u102c\u1038 ( B <sub>1<\/sub> \u104a B <sub>2<\/sub> \u104a B <sub>3<\/sub> ) \u104a \u1024 vector \u1014\u103e\u1005\u103a\u1001\u102f\u104f cross product \u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a<\/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;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b vector \u1019\u103b\u102c\u1038\u101b\u103e\u102d\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Vector A- (\u1041\u104a \u1042\u104a \u1043)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Vector B- (\u1044\u104a \u1045\u104a \u1046)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1024 vector \u1019\u103b\u102c\u1038 \u104f cross product \u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a \u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a = [(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;\">\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a\u1019\u103b\u102c\u1038 = [(2*6) \u2013 (3*5), (3*4) \u2013 (1*6), (1*5) \u2013 (2*4)]<\/span><\/li>\n<li> <span style=\"color: #000000;\">Cross product = (-3, 6, -3)\u104a<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">R \u1010\u103d\u1004\u103a vector \u1014\u103e\u1005\u103a\u1001\u102f\u104f cross product \u1000\u102d\u102f\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1014\u103e\u1005\u103a\u1001\u102f\u1011\u1032\u1019\u103e \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u101e\u1004\u103a\u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038 1- pracma package \u104f cross() function \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/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>\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038 2- \u101e\u1004\u1037\u103a\u1000\u102d\u102f\u101a\u103a\u1015\u102d\u102f\u1004\u103a\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u104b<\/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;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1021\u101e\u102f\u1036\u1038\u1001\u103b\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c 1- pracma package \u104f cross() function \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a vector \u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038\u101b\u103e\u102d cross product \u1000\u102d\u102f\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a <a href=\"https:\/\/cran.r-project.org\/web\/packages\/pracma\/index.html\" target=\"_blank\" rel=\"noopener\">pracma<\/a> package \u1019\u103e <strong>cross()<\/strong> function \u1000\u102d\u102f\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1019\u100a\u103a\u1000\u102d\u102f\u1015\u103c\u101e\u101e\u100a\u103a-<\/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;\">\u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a\u101e\u100a\u103a <strong>(-3\u104a 6\u104a -3)<\/strong> \u101f\u1030\u104d\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1005\u1031\u102c\u1015\u102d\u102f\u1004\u103a\u1038\u1000 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1000\u102d\u102f\u101a\u103a\u1010\u102d\u102f\u1004\u103a\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c 2- \u101e\u1004\u1037\u103a\u1000\u102d\u102f\u101a\u103a\u1015\u102d\u102f\u1004\u103a\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a vectors \u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038\u101b\u103e\u102d cross product \u1000\u102d\u102f\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u101e\u1004\u1037\u103a\u1000\u102d\u102f\u101a\u103a\u1015\u102d\u102f\u1004\u103a function \u1000\u102d\u102f\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f\u1015\u103c\u101e\u101e\u100a\u103a-<\/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;\">\u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a\u101e\u100a\u103a <strong>(-3\u104a 6\u104a -3)<\/strong> \u101f\u1030\u104d\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u101e\u100a\u103a \u101a\u1001\u1004\u103a\u1025\u1015\u1019\u102c\u1010\u103d\u1004\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a R \u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u1018\u102f\u1036\u1021\u101c\u102f\u1015\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a-<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-dot-\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a dot product \u1010\u103d\u1000\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-identity-matrix\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a identity matrix \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-\u1021\u101c\u103d\u1010\u103a\u1019\u1000\u103a\u1011\u101b\u1005\u103a\u1000\u102d\u102f-\u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a \u1021\u101c\u103d\u1010\u103a\u1019\u1000\u103a\u1011\u101b\u1005\u103a\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u100a\u103a\u1038<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a vector A \u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1012\u103c\u1015\u103a\u1005\u1004\u103a\u1019\u103b\u102c\u1038 (A 1 \u104a A 2 \u104a A 3 ) \u1014\u103e\u1004\u1037\u103a vector B \u1019\u103b\u102c\u1038 ( B 1 \u104a B 2 \u104a B 3 ) \u104a \u1024 vector \u1014\u103e\u1005\u103a\u1001\u102f\u104f cross product \u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a = [(A 2 *B 3 ) \u2013 (A 3 * B 2 ), (A 3 * B [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R - Statology \u1010\u103d\u1004\u103a \u101c\u1000\u103a\u101d\u102b\u1038\u1000\u1015\u103a\u1010\u102d\u102f\u1004\u103a\u1011\u102f\u1010\u103a\u1000\u102f\u1014\u103a\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f 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