{"id":501,"date":"2025-10-09T15:15:50","date_gmt":"2025-10-09T15:15:50","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus3\/?post_type=chapter&#038;p=501"},"modified":"2025-12-04T02:48:23","modified_gmt":"2025-12-04T02:48:23","slug":"three-dimensional-space-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus3\/chapter\/three-dimensional-space-apply-it\/","title":{"raw":"Three-Dimensional Space: Apply It","rendered":"Three-Dimensional Space: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Describe three-dimensional space mathematically<\/li>\r\n \t<li>Find and graph points in 3D space using their [latex](x, y, z)[\/latex] coordinates<\/li>\r\n \t<li>Write the distance formula in three dimensions<\/li>\r\n \t<li>Write the equations for simple planes and spheres<\/li>\r\n \t<li><span data-sheets-root=\"1\">Perform vector operations in \u211d3<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h3>Three-Dimensional Coordinate Systems<\/h3>\r\nYou're working as a designer for a company that creates custom storage solutions. A client has requested a modular shelving system for their office space, and you need to map out the positions of various connection points in 3D space to ensure everything fits together properly. The origin point [latex](0,0,0)[\/latex] represents the corner where two walls meet the floor. Distances are measured in feet, with the [latex]x[\/latex]-axis extending along one wall, the [latex]y[\/latex]-axis extending along the perpendicular wall, and the [latex]z[\/latex]-axis extending vertically from the floor.\r\n\r\n<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]316496[\/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]316497[\/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]316498[\/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]316499[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Describe three-dimensional space mathematically<\/li>\n<li>Find and graph points in 3D space using their [latex](x, y, z)[\/latex] coordinates<\/li>\n<li>Write the distance formula in three dimensions<\/li>\n<li>Write the equations for simple planes and spheres<\/li>\n<li><span data-sheets-root=\"1\">Perform vector operations in \u211d3<\/span><\/li>\n<\/ul>\n<\/section>\n<h3>Three-Dimensional Coordinate Systems<\/h3>\n<p>You&#8217;re working as a designer for a company that creates custom storage solutions. A client has requested a modular shelving system for their office space, and you need to map out the positions of various connection points in 3D space to ensure everything fits together properly. The origin point [latex](0,0,0)[\/latex] represents the corner where two walls meet the floor. Distances are measured in feet, with the [latex]x[\/latex]-axis extending along one wall, the [latex]y[\/latex]-axis extending along the perpendicular wall, and the [latex]z[\/latex]-axis extending vertically from the floor.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316496\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316496&theme=lumen&iframe_resize_id=ohm316496&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=\"ohm316497\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316497&theme=lumen&iframe_resize_id=ohm316497&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=\"ohm316498\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316498&theme=lumen&iframe_resize_id=ohm316498&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=\"ohm316499\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316499&theme=lumen&iframe_resize_id=ohm316499&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":14,"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-501","chapter","type-chapter","status-publish","hentry"],"part":420,"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\/501","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":10,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/501\/revisions"}],"predecessor-version":[{"id":2751,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/501\/revisions\/2751"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/420"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/501\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=501"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=501"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=501"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}