{"id":4085,"date":"2022-04-14T18:15:52","date_gmt":"2022-04-14T18:15:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/skills-review-for-vectors-in-three-dimensions\/"},"modified":"2022-11-09T16:31:34","modified_gmt":"2022-11-09T16:31:34","slug":"skills-review-for-vectors-in-three-dimensions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/skills-review-for-vectors-in-three-dimensions\/","title":{"raw":"Skills Review for Vectors in Three Dimensions","rendered":"Skills Review for Vectors in Three Dimensions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find the distance between two points<\/li>\r\n \t<li>Write the equation of a circle in standard form<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the Vectors in Three Dimensions section, we extend our understanding of vectors to three dimensions. Here we will review how to use the distance formula and write the equation of a circle in standard form.\r\n<h2>Find the Distance Between Two Points<\/h2>\r\n<strong><em>(See <a href=\"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/skills-review-for-vectors-in-the-plane\/\" target=\"_blank\" rel=\"noopener\">Module 2, Skills Review for Vectors in the Plane<\/a>)<\/em><\/strong>\r\n<h2>Write the Equation of a Circle in Standard Form<\/h2>\r\n<strong><em>(also in Module 1, Skills Review for Polar Coordinates)<\/em><\/strong>\r\n\r\nA circle is all points in a plane that are a fixed distance from a given point in the plane. The given point is called the <strong>center<\/strong>, (h,k), and the fixed distance is called the <strong>radius<\/strong>, r, of the circle.\r\n\r\nGiven a circle with center (h,k) and radius r, the equation of the circle in standard form is:\r\n<p style=\"text-align: center;\">[latex](x-h)^2+(y-k)^2=r^2[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>Example: Writing the Equation of a Circle in Standard Form<\/h3>\r\nWrite the equation of a circle in standard form with a center of (5,7) and a radius of 4.\r\n\r\n[reveal-answer q=\"18285444\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"18285444\"]\r\n<p style=\"text-align: left;\">Standard form of a circle is\u00a0[latex](x-h)^2+(y-k)^2=r^2[\/latex]. In this case, [latex]h=5[\/latex], [latex]k=7[\/latex], and [latex]r=4[\/latex].<\/p>\r\nTherefore, the equation of the circle in standard form is:\r\n<p style=\"text-align: center;\">[latex](x-5)^2+(y-7)^2=(4)^2[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex](x-5)^2+(y-7)^2=16[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nWrite the equation of a circle in standard form with a center of [latex](4,-2)[\/latex] and a radius of [latex]3[\/latex].\r\n\r\n[reveal-answer q=\"182854444\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"182854444\"]\r\n<p style=\"text-align: left;\">[latex](x-4)^2+(y+2)^2=9[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the distance between two points<\/li>\n<li>Write the equation of a circle in standard form<\/li>\n<\/ul>\n<\/div>\n<p>In the Vectors in Three Dimensions section, we extend our understanding of vectors to three dimensions. Here we will review how to use the distance formula and write the equation of a circle in standard form.<\/p>\n<h2>Find the Distance Between Two Points<\/h2>\n<p><strong><em>(See <a href=\"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/skills-review-for-vectors-in-the-plane\/\" target=\"_blank\" rel=\"noopener\">Module 2, Skills Review for Vectors in the Plane<\/a>)<\/em><\/strong><\/p>\n<h2>Write the Equation of a Circle in Standard Form<\/h2>\n<p><strong><em>(also in Module 1, Skills Review for Polar Coordinates)<\/em><\/strong><\/p>\n<p>A circle is all points in a plane that are a fixed distance from a given point in the plane. The given point is called the <strong>center<\/strong>, (h,k), and the fixed distance is called the <strong>radius<\/strong>, r, of the circle.<\/p>\n<p>Given a circle with center (h,k) and radius r, the equation of the circle in standard form is:<\/p>\n<p style=\"text-align: center;\">[latex](x-h)^2+(y-k)^2=r^2[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>Example: Writing the Equation of a Circle in Standard Form<\/h3>\n<p>Write the equation of a circle in standard form with a center of (5,7) and a radius of 4.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q18285444\">Show Solution<\/span><\/p>\n<div id=\"q18285444\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: left;\">Standard form of a circle is\u00a0[latex](x-h)^2+(y-k)^2=r^2[\/latex]. In this case, [latex]h=5[\/latex], [latex]k=7[\/latex], and [latex]r=4[\/latex].<\/p>\n<p>Therefore, the equation of the circle in standard form is:<\/p>\n<p style=\"text-align: center;\">[latex](x-5)^2+(y-7)^2=(4)^2[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex](x-5)^2+(y-7)^2=16[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Write the equation of a circle in standard form with a center of [latex](4,-2)[\/latex] and a radius of [latex]3[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q182854444\">Show Solution<\/span><\/p>\n<div id=\"q182854444\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: left;\">[latex](x-4)^2+(y+2)^2=9[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4085\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Calculus Volume 1. <strong>Provided by<\/strong>: Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.lumenlearning.com\/calculus1\/\">https:\/\/courses.lumenlearning.com\/calculus1\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Calculus Volume 2. <strong>Provided by<\/strong>: Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.lumenlearning.com\/calculus2\/\">https:\/\/courses.lumenlearning.com\/calculus2\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":349141,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Calculus Volume 1\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"https:\/\/courses.lumenlearning.com\/calculus1\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Calculus Volume 2\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"https:\/\/courses.lumenlearning.com\/calculus2\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4085","chapter","type-chapter","status-publish","hentry"],"part":4109,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4085","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4085\/revisions"}],"predecessor-version":[{"id":4713,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4085\/revisions\/4713"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/4109"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4085\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4085"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4085"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4085"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}