{"id":10809,"date":"2016-06-28T10:13:27","date_gmt":"2016-06-28T02:13:27","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=10809"},"modified":"2017-03-05T11:43:33","modified_gmt":"2017-03-05T03:43:33","slug":"intersection-3-planes-point-3d-interactive-graph","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/intersection-3-planes-point-3d-interactive-graph-10809","title":{"rendered":"Intersection of 3 planes at a point: 3D interactive graph"},"content":{"rendered":"

I recently developed an interactive 3D planes app<\/a> that demonstrates the concept of the solution of a system of 3 equations in 3 unknowns<\/strong> which is represented graphically as the intersection of 3 planes at a point<\/strong>.<\/p>\n

We learn to use determinants<\/a> and matrices<\/a> to solve such systems, but it's not often clear what it means in a geometric sense. Most of us struggle to conceive of 3D mathematical objects. <\/p>\n

Technology to the rescue.<\/p>\n

The new app allows you to explore the concepts of solving 3 equations by allowing you to see one plane at a time, two at a time, or all three, and the intersection point. You can also rotate it around to see it from different directions, and zoom in or out.<\/p>\n

Here's a screen shot: <\/p>\n

\"3<\/a>
\n Three planes intersecting at a point<\/div>\n

On the other hand, solving systems of 2 equations in 2 unknowns is represented by the intersection of 2 lines (or curves), which is relatively more straightforward. <\/p>\n

The link again:<\/p>\n

\n

Systems of 3×3 Equations interactive applet<\/a> <\/p>\n<\/blockquote>\n

See the 1 Comment<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"

\"solution<\/a>
\nThis 3D planes applet allows you to explore the concept of geometrically solving 3 equations in 3 unknowns.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[134,109,127],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/10809"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=10809"}],"version-history":[{"count":1,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/10809\/revisions"}],"predecessor-version":[{"id":11162,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/10809\/revisions\/11162"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=10809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=10809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=10809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}