{"id":1008,"date":"2025-02-11T13:09:01","date_gmt":"2025-02-11T18:09:01","guid":{"rendered":"https:\/\/brainfood-online.ca\/wp\/?p=1008"},"modified":"2025-02-16T19:38:54","modified_gmt":"2025-02-17T00:38:54","slug":"1008","status":"publish","type":"post","link":"https:\/\/brainfood-online.ca\/wp\/2025\/02\/11\/1008\/","title":{"rendered":"Vectors and Desmos in 3D"},"content":{"rendered":"<p>Recently, I&#8217;ve been working with Desmos in 3D. It is easy to perform a number of vector operations:<\/p>\n<ul>\n<li>defining a vector in 3D<\/li>\n<li>multiplying a vector by a scalar<\/li>\n<li>magnitude of a vector<\/li>\n<li>dot product<\/li>\n<li>cross product<\/li>\n<li>graphs of vectors are shown in 3D in a rotatable cube<\/li>\n<li>learn more here: <a style=\"color: #9d1fd4; text-decoration: underline;\" href=\"https:\/\/www.desmos.com\/calculator\/fk1xh0lgnn\">https:\/\/www.desmos.com\/calculator\/fk1xh0lgnn<\/a><\/li>\n<li><em>some of the applications described below have also been added to the link<\/em><\/li>\n<\/ul>\n<p>I also did some work on algebraic computations with 3D vectors, creating functions in (original) Desmos used in the following applications:<\/p>\n<ul>\n<li>converting angles between radians and degrees<\/li>\n<li>computing vector magnitude<\/li>\n<li>adding 3D vectors (algebraically)<\/li>\n<li>dot product<\/li>\n<li>cross product<\/li>\n<li>area of parallelogram bounded by two vectors<\/li>\n<li>scalar projection<\/li>\n<li>vector projection<\/li>\n<li>angle of a vector to the <em>x<\/em>, <em>y<\/em> and <em>z<\/em> axes<\/li>\n<li>angle between two vectors<\/li>\n<li>learn more here: <a style=\"color: #9d1fd4; text-decoration: underline;\" href=\"https:\/\/www.desmos.com\/calculator\/m9ac0d00qa\">https:\/\/www.desmos.com\/calculator\/m9ac0d00qa<\/a><\/li>\n<li><em>2D vectors may be manipulated using the 3D functions by setting the z components of vectors to zero<\/em><\/li>\n<\/ul>\n<p>Thinking about the vectors curriculum in <em>Grade 12 Calculus and Vectors<\/em>, <em>MCV4U<\/em>, it may be a useful exercise for classroom teachers to have students create and use functions like these &#8212; operationalizing them to demonstrate their correct implementation and use.<\/p>\n<p>Here is a useful video introducing 3D Desmos:<\/p>\n<p style=\"text-align: center;\"><iframe loading=\"lazy\" title=\"Intro to Desmos 3D Calculator\" src=\"https:\/\/www.youtube.com\/embed\/vMqtcDzhqUk\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recently, I&#8217;ve been working with Desmos in 3D. It is easy to perform a number of vector operations: defining a vector in 3D multiplying a vector by a scalar magnitude of a vector dot product cross product graphs of vectors are shown in 3D in a rotatable cube learn more&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[97,96,5,95],"tags":[98,99,101,100],"class_list":["post-1008","post","type-post","status-publish","format-standard","hentry","category-desmos","category-desmos-3d","category-mathematics","category-vectors","tag-desmos","tag-desmos-3d","tag-mcv4u","tag-vectors","loop-entry clr boxed"],"_links":{"self":[{"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/posts\/1008","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/comments?post=1008"}],"version-history":[{"count":9,"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/posts\/1008\/revisions"}],"predecessor-version":[{"id":1020,"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/posts\/1008\/revisions\/1020"}],"wp:attachment":[{"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/media?parent=1008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/categories?post=1008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brainfood-online.ca\/wp\/wp-json\/wp\/v2\/tags?post=1008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}