{"id":9406,"date":"2019-03-14T16:09:24","date_gmt":"2019-03-14T10:39:24","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9406"},"modified":"2019-03-14T16:09:24","modified_gmt":"2019-03-14T10:39:24","slug":"introduction-to-3-d-geometry-class-11-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/introduction-to-3-d-geometry-class-11-notes-mathematics\/","title":{"rendered":"Introduction To 3-D Geometry class 11 Notes Mathematics"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 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\" style=\"cursor:inherit\">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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-to-3-d-geometry-class-11-notes-mathematics\/#CBSE_Guide_Introduction_To_3-D_Geometry_class_11_Notes\" >CBSE Guide Introduction To 3-D Geometry class 11 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-to-3-d-geometry-class-11-notes-mathematics\/#Introduction_To_3-D_Geometry_class_11_Notes_Mathematics\" >Introduction To 3-D Geometry class 11 Notes Mathematics<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-to-3-d-geometry-class-11-notes-mathematics\/#Download_Revision_Notes_as_PDF\" >Download Revision Notes as PDF\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-to-3-d-geometry-class-11-notes-mathematics\/#Introduction_To_3-D_Geometry_class_11_Notes\" >Introduction To 3-D Geometry class 11 Notes<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-to-3-d-geometry-class-11-notes-mathematics\/#CBSE_Class-11_Revision_Notes_and_Key_Points\" >CBSE Class-11 Revision Notes and Key Points<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>CBSE Mathematics Chapter 12 Introduction To 3-D Geometry class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Introduction To 3-D Geometry class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE board exams and school based annual examinations. Class 11 Mathematics notes on Chapter 12 Introduction To 3-D Geometry class 11 Notes Mathematics are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Guide_Introduction_To_3-D_Geometry_class_11_Notes\"><\/span>CBSE Guide Introduction To 3-D Geometry class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 11 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_To_3-D_Geometry_class_11_Notes_Mathematics\"><\/span>Introduction To 3-D Geometry class 11 Notes Mathematics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 11th revision notes for Chapter 12 Introduction To 3-D Geometry class 11 Notes Mathematics in PDF format for free. Download revision notes for Introduction To 3-D Geometry class 11 Notes Mathematics and score high in exams. These are the Introduction To 3-D Geometry class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.<\/p>\n<h1 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"Download_Revision_Notes_as_PDF\"><\/span><a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF\u00a0<\/a><span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p style=\"text-align: center;\"><strong>CBSE Class 11 Mathematics<br \/>\nRevision Notes<br \/>\nChapter-12<br \/>\nIntroduction To 3-D Geometry class 11 Notes Mathematics<br \/>\n<\/strong><\/p>\n<hr \/>\n<ol>\n<li><strong>Coordinates- axes, planes, points in 3D<\/strong><\/li>\n<li><strong>Distance between Two Points <\/strong><\/li>\n<li><strong>Section Formula <\/strong><\/li>\n<\/ol>\n<ul>\n<li><strong>Coordinate axes<\/strong>: In three dimensions, the coordinate axes of a rectangular Cartesian coordinate system are three mutually perpendicular lines. The axes are called the x-axis, y-axis and z-axis.<\/li>\n<li><strong>Planes<\/strong>: The three planes determined by the pair of axes are the coordinate planes, called XY, YZ and ZX planes.<\/li>\n<\/ul>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?xy-\" \/><\/span><\/span>plane i.e., <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?z = 0\" \/><\/span><\/span><\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?yz-\" \/><\/span><\/span>plane i.e., <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x = 0\" \/><\/span><\/span><\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?zx-\" \/><\/span><\/span>plane i.e., <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y=0\" \/><\/span><\/span><\/p>\n<ul>\n<li><strong>Octants<\/strong>: The three coordinate planes divide the space into eight parts known as octants.<\/li>\n<li><strong>Points in 3D<\/strong>: The coordinates of a point P in three dimensional geometry is always written in the form of triplet like (x, y, z). Here x, y\u00a0 and z are the distances from the YZ, ZX and\u00a0 XY<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{Any point on}}\\;{\\text{XY }} \\to {\\text{ plane}}\\;\\;\\left( {{\\text{ x}},{\\text{ y}},{\\text{ }}0} \\right)\" \/><\/span><\/span><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{Any point on}}\\;{\\text{YZ }} \\to {\\text{plane}}\\;\\;\\;\\;\\left( {{\\text{ }}0,{\\text{ y}},{\\text{ z}}} \\right)\" \/><\/span><\/span><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{Any point on}}\\;{\\text{ZX }} \\to {\\text{plane}}\\;\\;\\;\\left( {{\\text{ x}},{\\text{ }}0,{\\text{z}}} \\right)\" \/><\/span><\/span><\/li>\n<\/ul>\n<ul>\n<li><strong>Distance formula between two points<\/strong>: Distance between two points <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{P }\\left( \\text{ }{{\\text{x}}_{1}}\\text{ },\\text{ }{{\\text{y}}_{1}},\\text{ }{{\\text{z}}_{1}}\\text{ } \\right)\\text{ and}~\\text{Q }\\left( \\text{ }{{\\text{x}}_{2}}\\text{ },\\text{ }{{\\text{y}}_{2}}\\text{ },{{\\text{z}}_{2}}\\text{ } \\right)\\text{ is}~\" \/><\/span><\/span><\/li>\n<\/ul>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left| \\text{PQ} \\right|\" \/><\/span><\/span><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{ }=\\text{ }\\sqrt{{{\\left( ~{{x}_{2}}-{{x}_{1}}~ \\right)}^{2}}+~\\left( ~{{y}_{2}}-{{y}_{1}}{{)}^{2}} \\right)+~{{\\left( ~{{z}_{2}}-{{z}_{1}} \\right)}^{2}}}~\" \/><\/span><\/span><\/p>\n<p><strong>Section Formula<\/strong>: The co-ordinates of R which divides a line segment joining the points <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?~~~~\\text{P }\\left( \\text{ }{{\\text{x}}_{1}}\\text{ },\\text{ }{{\\text{y}}_{1}},\\text{ }{{\\text{z}}_{1}}\\text{ } \\right)\\text{ and}~\\text{Q }\\left( \\text{ }{{\\text{x}}_{2}}\\text{ },\\text{ }{{\\text{y}}_{2}},\\text{ }{{\\text{z}}_{2}}\\text{ } \\right)~\" \/><\/span><\/span><\/p>\n<p>Internally and externally in the ratio m : n respectively<\/p>\n<p>Internally:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?R\\left( \\frac{m{{x}_{2}}+n{{x}_{1}}}{m+n},\\frac{m{{y}_{2}}+n{{y}_{1}}}{m+n},\\frac{m{{z}_{2}}+n{{z}_{1}}}{m+n} \\right)\" \/><\/span><\/span><\/p>\n<p>Externally:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?S\\left( \\frac{m{{x}_{2}}-n{{x}_{1}}}{m-n},\\frac{m{{y}_{2}}-n{{y}_{1}}}{m-n},\\frac{m{{z}_{2}}-n{{z}_{1}}}{m-n} \\right)\" \/><\/span><\/span><\/p>\n<p><strong>Centroid<\/strong>: The coordinates of the centroid of the trinagle whose vertices are <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?~~~~\\left( \\text{ }{{\\text{x}}_{1}}\\text{ },\\text{ }{{\\text{y}}_{1}},\\text{ }{{\\text{z}}_{1}}\\text{ } \\right)\\text{ }\" \/><\/span><\/span><\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?~\\left( \\text{ }{{\\text{x}}_{2}}\\text{ },\\text{ }{{\\text{y}}_{2}},\\text{ }{{\\text{z}}_{2}}\\text{ } \\right)\\ \\ \\ ~and\\ \\ \\ ({{x}_{3}},\\ {{y}_{3}},{{z}_{3}})\" \/><\/span><\/span>\u00a0is<\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left( \\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3},\\frac{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}}{3} \\right)\" \/><\/span><\/span><\/p>\n<h1><span class=\"ez-toc-section\" id=\"Introduction_To_3-D_Geometry_class_11_Notes\"><\/span>Introduction To 3-D Geometry class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<ul>\n<li>CBSE Revision notes (PDF Download) Free<\/li>\n<li>CBSE Revision notes for Class 11 Mathematics PDF<\/li>\n<li>CBSE Revision notes Class 11 Mathematics \u2013 CBSE<\/li>\n<li>CBSE Revisions notes and Key Points Class 11 Mathematics<\/li>\n<li>Summary of the NCERT books all chapters in Mathematics class 11<\/li>\n<li>Short notes for CBSE class 11th Mathematics<\/li>\n<li>Key notes and chapter summary of Mathematics class 11<\/li>\n<li>Quick revision notes for CBSE board exams<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-11_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-11 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Introduction To 3-D Geometry class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-physics\/1340\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-mathematics\/1371\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-biology\/1388\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-accountancy\/1411\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-economics\/1423\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-business-studies\/1740\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-computer-science\/1852\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-informatics-practices\/1874\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-geography\/1864\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Geography<\/a><\/li>\n<\/ul>\n<p>To download Introduction To 3-D Geometry class 11 Notes, sample paper for class 11 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Mathematics Chapter 12 Introduction To 3-D Geometry class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Introduction To 3-D Geometry class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE board exams and school based annual examinations. &#8230; <a title=\"Introduction To 3-D Geometry class 11 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-to-3-d-geometry-class-11-notes-mathematics\/\" aria-label=\"More on Introduction To 3-D Geometry class 11 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":9298,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,456],"tags":[457,150,590,461,426,240],"class_list":["post-9406","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-11","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-introduction-to-3-d-geometry","tag-mathematics-notes","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Introduction To 3-D Geometry class 11 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Introduction To 3-D Geometry class 11 Notes Mathematics Chapter 12 in PDF format for free download. 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