{"id":531,"date":"2025-10-09T15:18:45","date_gmt":"2025-10-09T15:18:45","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus3\/?post_type=chapter&#038;p=531"},"modified":"2025-12-05T02:15:43","modified_gmt":"2025-12-05T02:15:43","slug":"lines-and-planes-in-space-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus3\/chapter\/lines-and-planes-in-space-apply-it\/","title":{"raw":"Lines and Planes in Space: Apply It","rendered":"Lines and Planes in Space: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Write different types of equations (vector, parametric, symmetric) to describe lines in space<\/li>\r\n \t<li>Find the distance from a point to a given line<\/li>\r\n \t<li>Write equations for planes using vectors and scalars<\/li>\r\n \t<li>Find the angle between two planes<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong> Mapping Data Center Cable Routes in Three Dimensions<\/strong><\/h2>\r\n<p class=\"font-claude-response-body whitespace-normal break-words\">You work as a junior technician for a company that maintains a multi-floor data center. The building has three floors, and your team needs to plan cable routes and network equipment placement using a 3D coordinate system. The origin is at the northwest corner of the ground floor, with the [latex]x[\/latex]-axis pointing east, the [latex]y[\/latex]-axis pointing south, and the [latex]z[\/latex]-axis pointing up (all measurements in meters).<\/p>\r\n<p class=\"font-claude-response-body whitespace-normal break-words\">Your supervisor has given you a facilities map with coordinates for server racks, network switches, and cable entry points. You need to write equations for straight cable runs between equipment, calculate distances to verify cable length requirements, and determine the angles between equipment planes to ensure proper ventilation spacing. This planning work ensures the data center runs efficiently\u2014supporting everything from online classes to hospital records to small business websites that people from all walks of life depend on every day.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<div>\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0\">\r\n<p class=\"font-claude-response-body whitespace-normal break-words\">[ohm_question hide_question_numbers=1]316574[\/ohm_question]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div>\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0\"><\/div>\r\n<\/div>\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"font-claude-response-body whitespace-normal break-words\">[ohm_question hide_question_numbers=1]316583[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"font-claude-response-body whitespace-normal break-words\">[ohm_question hide_question_numbers=1]316586[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"font-claude-response-body whitespace-normal break-words\">[ohm_question hide_question_numbers=1]316589[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"font-claude-response-body whitespace-normal break-words\">[ohm_question hide_question_numbers=1]316590[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Write different types of equations (vector, parametric, symmetric) to describe lines in space<\/li>\n<li>Find the distance from a point to a given line<\/li>\n<li>Write equations for planes using vectors and scalars<\/li>\n<li>Find the angle between two planes<\/li>\n<\/ul>\n<\/section>\n<h2><strong> Mapping Data Center Cable Routes in Three Dimensions<\/strong><\/h2>\n<p class=\"font-claude-response-body whitespace-normal break-words\">You work as a junior technician for a company that maintains a multi-floor data center. The building has three floors, and your team needs to plan cable routes and network equipment placement using a 3D coordinate system. The origin is at the northwest corner of the ground floor, with the [latex]x[\/latex]-axis pointing east, the [latex]y[\/latex]-axis pointing south, and the [latex]z[\/latex]-axis pointing up (all measurements in meters).<\/p>\n<p class=\"font-claude-response-body whitespace-normal break-words\">Your supervisor has given you a facilities map with coordinates for server racks, network switches, and cable entry points. You need to write equations for straight cable runs between equipment, calculate distances to verify cable length requirements, and determine the angles between equipment planes to ensure proper ventilation spacing. This planning work ensures the data center runs efficiently\u2014supporting everything from online classes to hospital records to small business websites that people from all walks of life depend on every day.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<div>\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316574\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316574&theme=lumen&iframe_resize_id=ohm316574&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<\/div>\n<div>\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0\"><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316583\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316583&theme=lumen&iframe_resize_id=ohm316583&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316586\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316586&theme=lumen&iframe_resize_id=ohm316586&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316589\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316589&theme=lumen&iframe_resize_id=ohm316589&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316590\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316590&theme=lumen&iframe_resize_id=ohm316590&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":16,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-531","chapter","type-chapter","status-publish","hentry"],"part":422,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":9,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/531\/revisions"}],"predecessor-version":[{"id":2758,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/531\/revisions\/2758"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/422"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/531\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=531"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=531"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=531"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}