{"id":383,"date":"2015-11-12T19:43:17","date_gmt":"2015-11-12T18:43:17","guid":{"rendered":"http:\/\/devnot.wordpress.com\/?p=383"},"modified":"2022-01-29T12:02:41","modified_gmt":"2022-01-29T11:02:41","slug":"get-the-distance-between-a-point-and-a-vector","status":"publish","type":"post","link":"https:\/\/thomas-jansen.eu\/?p=383","title":{"rendered":"Get the distance between a point and vector (2D)"},"content":{"rendered":"\n\n\n<p>Determine the distance of point&nbsp;P and vector through points P1, P2<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"http:\/\/510245153.swh.strato-hosting.eu\/wp-content\/uploads\/2012\/03\/pointvect2d.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomasjansen.eu\/wp-content\/uploads\/2019\/12\/wp_dist_point_vector.svg\" alt=\"\" class=\"wp-image-567\" width=\"372\" height=\"245\"\/><\/a><figcaption>Distance point &#8211; vector<\/figcaption><\/figure>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-be7cfbe6e93c9ab1ead40c8abd7f2749_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#100;&#105;&#115;&#116;&#32;&#61;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#32;&#124;&#32;&#40;&#66;&#95;&#120;&#32;&#45;&#32;&#65;&#95;&#120;&#41;&#32;&#40;&#80;&#95;&#121;&#32;&#45;&#32;&#65;&#95;&#121;&#41;&#32;&#45;&#32;&#40;&#66;&#95;&#121;&#32;&#45;&#32;&#65;&#95;&#121;&#41;&#32;&#40;&#80;&#95;&#120;&#32;&#45;&#32;&#65;&#95;&#120;&#41;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#32;&#124;&#125;&#123;&#124;&#124;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#66;&#125;&#124;&#124;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"399\" style=\"vertical-align: -18px;\"\/><\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>This is a &#8216;2D cross product&#8217; of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-01e3f48fa11a50273e3889539222abe7_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"28\" style=\"vertical-align: 0px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-e4e0d20db5df255dd17295ac3323b8bb_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#80;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"28\" style=\"vertical-align: 0px;\"\/>. Since the cross product is the parallelogram surface of the two vectors, dividing it by the length of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-01e3f48fa11a50273e3889539222abe7_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"28\" style=\"vertical-align: 0px;\"\/> to get the distance.<\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-89e83680f515e977c685d71da9edca51_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#124;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#66;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#124;&#32;&#61;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#40;&#66;&#95;&#120;&#32;&#45;&#32;&#65;&#95;&#120;&#41;&#94;&#50;&#32;&#43;&#32;&#40;&#66;&#95;&#121;&#32;&#45;&#32;&#65;&#95;&#121;&#41;&#94;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"282\" style=\"vertical-align: -7px;\"\/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determine the distance of point&nbsp;P and vector through points P1, P2 $dist = \\dfrac{\\left | (B_x &#8211; A_x) (P_y &#8211; A_y) &#8211; (B_y &#8211; A_y) (P_x &#8211; A_x) \\right |}{||\\overline{AB}||}$ This is a &#8216;2D cross product&#8217; of $\\overline{AB}$ and $\\overline{AP}$. Since the cross product is the parallelogram surface of the two vectors, dividing it by [&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":[],"class_list":["post-383","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/383","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=383"}],"version-history":[{"count":2,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/383\/revisions"}],"predecessor-version":[{"id":663,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/383\/revisions\/663"}],"wp:attachment":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}