{"id":156550,"date":"2022-03-26T01:52:53","date_gmt":"2022-03-25T20:22:53","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/perpendicular-distance-of-a-point-from-a-plane\/"},"modified":"2025-06-24T14:27:39","modified_gmt":"2025-06-24T08:57:39","slug":"perpendicular-distance-of-a-point-from-a-plane","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/perpendicular-distance-of-a-point-from-a-plane\/","title":{"rendered":"Perpendicular Distance Of A Point From A Plane"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/perpendicular-distance-of-a-point-from-a-plane\/#Perpendicular_Distance_of_a_Point_From_a_Line_in_3D\" title=\"Perpendicular Distance of a Point From a Line in 3D\">Perpendicular Distance of a Point From a Line in 3D<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/perpendicular-distance-of-a-point-from-a-plane\/#Distance_of_a_Point_From_a_Plane_Using_Vector_Form\" title=\"Distance of a Point From a Plane Using Vector Form\">Distance of a Point From a Plane Using Vector Form<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/perpendicular-distance-of-a-point-from-a-plane\/#Distance_of_a_Point_from_a_Plane_with_the_Help_of_Cartesian_Form\" title=\"Distance of a Point from a Plane with the Help of Cartesian Form\">Distance of a Point from a Plane with the Help of Cartesian Form<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/perpendicular-distance-of-a-point-from-a-plane\/#The_Perpendicular_Distance_from_a_Point_to_a_Line_3D\" title=\"The Perpendicular Distance from a Point to a Line 3D\">The Perpendicular Distance from a Point to a Line 3D<\/a><\/li><\/ul><\/nav><\/div>\n<h1>Basics of Perpendicularity<\/h1>\n<p>A line is perpendicular to a plane if it intersects the plane at a right angle. The line is perpendicular to the plane if the angle between the line and the plane is 90 degrees. Perpendicular Distance Of A Point From A Plane.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156549 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/perpendicular-distance-of-a-point-from-a-plane.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/perpendicular-distance-of-a-point-from-a-plane.jpg?v=1648239771 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/perpendicular-distance-of-a-point-from-a-plane-300x212.jpg?v=1648239771 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Perpendicular_Distance_of_a_Point_From_a_Line_in_3D\"><\/span>Perpendicular Distance of a Point From a Line in 3D<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The perpendicular distance of a point from a line in 3D is the distance from the point to the line measured perpendicular to the line. This can be calculated using the Pythagorean theorem.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Distance_of_a_Point_From_a_Plane_Using_Vector_Form\"><\/span>Distance of a Point From a Plane Using Vector Form<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The distance between a point and a plane can be found by using the formula:<\/p>\n<p>Distance = (Vector A.x &#8211; Vector B.x)2 + (Vector A.y &#8211; Vector B.y)2<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Distance_of_a_Point_from_a_Plane_with_the_Help_of_Cartesian_Form\"><\/span>Distance of a Point from a Plane with the Help of Cartesian Form<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Given a point and a plane in Cartesian form, the distance between the point and the plane can be found using the following formula:<\/p>\n<p>\\(\\delta=\\frac{|x-a|+|y-b|}{2}\\),<\/p>\n<p>where \\(a\\) and \\(b\\) are the coordinates of the point and the plane, respectively, and \\(\\delta\\) is the distance between the point and the plane.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Perpendicular_Distance_from_a_Point_to_a_Line_3D\"><\/span>The Perpendicular Distance from a Point to a Line 3D<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The perpendicular distance from a point to a line in three dimensions is the distance from the point to the line that is perpendicular to the line.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Basics of Perpendicularity A line is perpendicular to a plane if it intersects the plane at a right angle. The [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Perpendicular Distance Of A Point From A Plane","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Perpendicular Distance Of A Point From A Plane in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/perpendicular-distance-of-a-point-from-a-plane\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Perpendicular Distance Of A Point From A Plane - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Perpendicular Distance Of A Point From A Plane in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/perpendicular-distance-of-a-point-from-a-plane\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Perpendicular Distance Of A Point From A Plane - 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