{"id":379,"date":"2015-12-12T19:30:18","date_gmt":"2015-12-12T18:30:18","guid":{"rendered":"http:\/\/devnot.wordpress.com\/?p=379"},"modified":"2022-01-29T12:00:55","modified_gmt":"2022-01-29T11:00:55","slug":"determine-whether-a-point-is-above-or-below-a-vector2d","status":"publish","type":"post","link":"https:\/\/thomas-jansen.eu\/?p=379","title":{"rendered":"Determine whether a point is above or below a vector (2D)"},"content":{"rendered":"\n\n\n<p>Determine whether point P is above or below a vector through points A, B<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomasjansen.eu\/wp-content\/uploads\/2019\/12\/wp_point_above_vector-1.svg\" alt=\"\" class=\"wp-image-562\" width=\"351\" height=\"230\"\/><figcaption>Point above vector<br><\/figcaption><\/figure>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-6a0b41f6abe81b1bff79c93c9793e9cf_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#122;&#32;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"365\" style=\"vertical-align: -6px;\"\/><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Possible values for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-ec5583fa081a1e03212c151e3c222412_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>:<\/p>\n\n\n\n<p>0&nbsp;    On the vector<\/p>\n\n\n\n<p>&gt; 0  Above the vector<\/p>\n\n\n\n<p>&lt; 0  Below the vector<\/p>\n\n\n\n<p>The function above is the &#8216;2D cross product&#8217;, therefore z is the surface of vector <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;\"\/>. Dividing the surface by the length of vector  <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;\"\/>   (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-b346e304cb55d96dcd7f02307876caa1_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#92;&#118;&#101;&#114;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#66;&#125;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -4px;\"\/>) gives the &#8216;signed distance&#8217; of the point perpendicular to the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/thomas-jansen.eu\/wp-content\/ql-cache\/quicklatex.com-fda1e51b12ba3624074fcbebad72b1fc_l3.svg\" class=\"ql-img-inline-formula \" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determine whether point P is above or below a vector through points A, B $z = (B_x &#8211; A_x) (P_y &#8211; A_y) &#8211; (B_y &#8211; A_y) (P_x &#8211; A_x)$ Possible values for $z$: 0&nbsp; On the vector &gt; 0 Above the vector &lt; 0 Below the vector The function above is the &#8216;2D cross product&#8217;, [&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":[95],"class_list":["post-379","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-vector-point"],"_links":{"self":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/379","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=379"}],"version-history":[{"count":6,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/379\/revisions"}],"predecessor-version":[{"id":679,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/379\/revisions\/679"}],"wp:attachment":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}