Answer:<\/strong><\/p>\n\n\n\n Consider the point. (1, 3, 4) In three-dimensional Cartesian space, the location of any point is given by an ordered triple of coordinates (x, y, z). This space is fundamentally structured by three mutually perpendicular coordinate planes: the xy-plane, the yz-plane, and the xz-plane. The projection of a point onto one of these planes is the location where a perpendicular line from the point intersects the plane. This projected point can be thought of as the shadow cast by the original point onto the plane.<\/p>\n\n\n\n Projection onto the xy-Plane<\/strong><\/p>\n\n\n\n The xy-plane is the set of all points for which the z-coordinate is zero (z = 0). To project a point (x\u2080, y\u2080, z\u2080) onto this plane, one must find the point on the plane that is closest to it. This is achieved by dropping a perpendicular from the point to the plane. A line perpendicular to the xy-plane is parallel to the z-axis. Along such a line, the x and y-coordinates do not change. Therefore, the projection is found by simply setting the z-coordinate to zero. For the given point (1, 3, 4), its projection onto the xy-plane is (1, 3, 0).<\/p>\n\n\n\n Projection onto the yz-Plane<\/strong><\/p>\n\n\n\n The yz-plane is defined by the equation x = 0. A line perpendicular to this plane is parallel to the x-axis. To find the projection of a point (x\u2080, y\u2080, z\u2080) onto the yz-plane, the x-coordinate must be set to zero, while the y and z-coordinates are preserved. Applying this to the point (1, 3, 4), its x-coordinate of 1 is replaced with 0, yielding the projection (0, 3, 4).<\/p>\n\n\n\n Projection onto the xz-Plane<\/strong><\/p>\n\n\n\n Finally, the xz-plane consists of all points where the y-coordinate is zero (y = 0). A line perpendicular to the xz-plane is parallel to the y-axis. Consequently, projecting a point onto this plane involves retaining the original x and z-coordinates and setting the y-coordinate to zero. For the point (1, 3, 4), its projection onto the xz-plane is therefore (1, 0, 4).<\/p>\n\n\n\n Consider the point. (1, 3, 4) What is the projection of the point on the xy-plane? (x, y, z) = ) What is the projection of the point on the yz-plane? (x, y, z) = ) What is the projection of the point on the xz-plane? (x, y, z) = )Consider the point. (1, 3, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-231206","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=231206"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231206\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
What is the projection of the point on the xy-plane? (x, y, z) = (1, 3, 0)<\/strong>
What is the projection of the point on the yz-plane? (x, y, z) = (0, 3, 4)<\/strong>
What is the projection of the point on the xz-plane? (x, y, z) = (1, 0, 4)<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation<\/h3>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-855.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"