{"id":193,"date":"2011-05-29T12:12:27","date_gmt":"2011-05-29T12:12:27","guid":{"rendered":"http:\/\/devnot.wordpress.com\/?p=193"},"modified":"2011-05-29T12:12:27","modified_gmt":"2011-05-29T12:12:27","slug":"the-cross-product-and-some-uses","status":"publish","type":"post","link":"https:\/\/thomas-jansen.eu\/?p=193","title":{"rendered":"The cross product"},"content":{"rendered":"<p><a href=\"http:\/\/510245153.swh.strato-hosting.eu\/wp-content\/uploads\/2011\/05\/cross0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-194\" title=\"cross0\" src=\"http:\/\/510245153.swh.strato-hosting.eu\/wp-content\/uploads\/2011\/05\/cross0.png\" alt=\"\" width=\"123\" height=\"96\" \/><\/a><\/p>\n<p>Formula:<\/p>\n<p>Nx = ( dz1 * dy2 ) &#8211; (dy1 * dz2 );<br \/>\nNy = ( dx1 * dz2 ) &#8211; (dz1 * dx2 );<br \/>\nNz = ( dy1 * dx2 ) &#8211; (dx1 * dy2 );<br \/>\n<small><br \/>\ndx1 is the delta between the two x coordinates (last &#8211; first) of vector V1.<br \/>\ndx2 is the delta between the two x coordinates (last &#8211; first) of vector V2.<br \/>\ndy1 is the delta between the two y coordinates (last &#8211; first) of vector V1.<br \/>\ndy2 is the delta between the two y coordinates (last &#8211; first) of vector V2.<br \/>\ndz1 is the delta between the two z coordinates (last &#8211; first) of vector V1.<br \/>\ndz2 is the delta between the two z coordinates (last &#8211; first) of vector V2.<br \/>\n<\/small><\/p>\n<p>The cross product calculated between two vectors results in a vector perpendicular to both vectors. The length of this vector is the surface of the parallelogram.<\/p>\n<p>If the angle between the two vectors is 0 or 180 degrees the lengths is zero.\u00a0 This can be used for vector overlap checks.<\/p>\n<p>In 2D only the Nz value is used, it can be used for overlaps or parallel vectors etc.<\/p>\n<p>Uses:<\/p>\n<p><a title=\"Check whether two 2d vectors are\u00a0parallel\" href=\"http:\/\/devnot.wordpress.com\/2011\/09\/08\/check-whether-two-2d-vectors-are-parallel\/\">Are two 2D vectors parallel<\/a><\/p>\n<p><a title=\"Check whether two 2D vectors are\u00a0coincident.\" href=\"http:\/\/devnot.wordpress.com\/2011\/09\/08\/check-whether-two-2d-vectors-are-coincident\/\">Are two 2D vectors\u00a0 coincident<\/a><\/p>\n<p><a title=\"2D Line intersection using\u00a0vectors\" href=\"http:\/\/devnot.wordpress.com\/2011\/09\/08\/2d-line-intersection-using-vectors\/\">Get the intersection point of two 2D vectors<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Formula: Nx = ( dz1 * dy2 ) &#8211; (dy1 * dz2 ); Ny = ( dx1 * dz2 ) &#8211; (dz1 * dx2 ); Nz = ( dy1 * dx2 ) &#8211; (dx1 * dy2 ); dx1 is the delta between the two x coordinates (last &#8211; first) of vector V1. dx2 is the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[18],"class_list":["post-193","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-cross-vector"],"_links":{"self":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=193"}],"version-history":[{"count":0,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/193\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}