{"id":9350,"date":"2018-02-09T16:23:04","date_gmt":"2018-02-09T10:53:04","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9350"},"modified":"2019-03-02T17:13:00","modified_gmt":"2019-03-02T11:43:00","slug":"three-dimensional-geometry-class-12-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/three-dimensional-geometry-class-12-notes-mathematics\/","title":{"rendered":"Three Dimensional Geometry Class 12 Notes Mathematics"},"content":{"rendered":"<p><strong>Three Dimensional Geometry Class 12 Notes Mathematics<\/strong> in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Three Dimensional Geometry class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school-based annual examinations. Class 12 Mathematics notes on chapter 11 Three Dimensional Geometry are also available for download in CBSE Guide website.<\/p>\n<h2>Three Dimensional Geometry Class 12 Notes Mathematics<\/h2>\n<p>Download CBSE class 12th revision notes for chapter 11 Three Dimensional Geometry in PDF format for free. Download revision notes for Three Dimensional Geometry class 12 Notes and score high in exams. These are the Three Dimensional Geometry class 12 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter 11 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days.<\/p>\n<p style=\"text-align: center;\"><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><\/strong><\/p>\n<h2><strong>CBSE Class 12 Mathematics Revision Notes Chapter 11 Three Dimensional Geometry<br \/>\n<\/strong><\/h2>\n<ul>\n<li>Direction cosines of a line: Direction cosines of a line are the cosines of the angles made by the line with the positive directions of the coordinate axes.<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image001.png\" \/>are the direct ion cosines of a line, then\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image002.png\" \/><\/li>\n<li>Direct ion cosines of a line joining two points<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image003.png\" \/>and<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image004.png\" \/>are <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image005.png\" \/><\/li>\n<\/ul>\n<p>\u00b7\u00a0\u00a0 where\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image006.png\" alt=\"Three Dimensional Geometry Class 12 Notes Mathematics\" width=\"271\" height=\"33\" \/><\/p>\n<ul>\n<li>Direction ratios of a line are the numbers which are proportional to the direct ion cosines of a line.<\/li>\n<li>If \u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image007.png\" \/>are the direct ion cosines and \u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image008.png\" \/>\u00a0are the direct ion ratios of a line<\/li>\n<\/ul>\n<p>Then, <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image009.png\" \/>,<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image010.png\" \/>,<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image011.png\" \/><\/p>\n<ul>\n<li><strong>Skew lines<\/strong>: Skew lines are lines in space which are neither parallel nor intersecting. They lie in different planes.<\/li>\n<li><strong>Angle between two skew lines<\/strong>: Angle between skew lines is the angle between two intersecting lines drawn from any point (preferably through the origin) parallel to each of the skew lines.<\/li>\n<li>If <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image012.png\" \/>are the direction cosines of two lines; and <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image013.png\" \/>\u00a0is the acute angle between the two lines; then,<\/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?\\cos \\theta = \\left| {{{{a_1}{a_2} + {b_1}{b_2} + {c_1}_2} \\over {\\sqrt {a_1^2 + b_1^2 + c_1^2} \\sqrt {a_2^2 + b_2^2 + c_2^2} }}} \\right|\" \/><\/span><\/span><\/p>\n<ul>\n<li>Vector equation of a line that passes through the given point whose position vector is\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image015.png\" \/>\u00a0and parallel to a given vector <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image016.png\" \/><\/li>\n<li>Equation of a line through a point \u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image017.png\" \/>\u00a0\u00a0and having direct ion cosines\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image007.png\" \/>\u00a0is <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image018.png\" \/><\/li>\n<li>The vector equation of a line which passes through two points whose position vectors are\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image019.png\" \/><\/li>\n<li>Cartesian equation of a line that passes through two points <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image017.png\" \/>\u00a0and <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image020.png\" \/>\u00a0is\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image021.png\" \/><\/li>\n<li>If <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image013.png\" \/>\u00a0is the acute angle between <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image022.png\" \/>\u00a0and\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image023.png\" \/>\u00a0\u00a0then, <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?\\cos \\theta = \\left| {{{\\overrightarrow {{b_1}} \\overrightarrow {{b_2}} } \\over {\\left| {\\overrightarrow {{b_1}} } \\right|\\left| {\\overrightarrow {{b_2}} } \\right|}}} \\right|\" \/><\/span><\/span><\/li>\n<li>If\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image025.png\" \/>\u00a0\u00a0 and\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image026.png\" \/>are the equations of two lines, then the acute angle between the two lines is given by <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image027.png\" \/><\/li>\n<li>Shortest distance between two skew lines is the line segment perpendicular to both the lines.<\/li>\n<li>Shortest distance between <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?\\overrightarrow r = \\overrightarrow {{a_1}} + \\lambda \\overrightarrow {{b_1}}\" \/><\/span><\/span>\u00a0and <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?\\overrightarrow r = \\overrightarrow {{a_2}} + \\lambda \\overrightarrow {{b_2}}\" \/><\/span><\/span>\u00a0is <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| {{{\\left( {\\overrightarrow {{b_1}} \\times \\overrightarrow {{b_2}} } \\right).\\left( {\\overrightarrow {{a_2}} - \\overrightarrow {{a_1}} } \\right)} \\over {\\left| {{b_1} \\times {b_2}} \\right|}}} \\right|\" \/><\/span><\/span><\/li>\n<li>Shortest distance between the lines: <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image030.png\" \/>\u00a0\u00a0\u00a0and\u00a0\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image031.png\" \/>\u00a0is<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" id=\"Picture 1\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image032.png\" alt=\"Three Dimensional Geometry Class 12 Notes Mathematics\" width=\"428\" height=\"140\" \/><\/p>\n<ul>\n<li>Distance between parallel lines\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?\\overrightarrow r = \\overrightarrow {{a_1}} + \\lambda \\overrightarrow {{b_1}}\" \/><\/span><\/span>\u00a0and <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?\\overrightarrow r = \\overrightarrow {{a_2}} + \\lambda \\overrightarrow {{b_2}}\" \/><\/span><\/span>is <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left| {{{\\overrightarrow b \\times \\left( {\\overrightarrow {{a_2}} - \\overrightarrow {{a_1}} } \\right)} \\over {\\left| b \\right|}}} \\right|\" alt=\"Three Dimensional Geometry Class 12 Notes Mathematics\" width=\"114\" height=\"54\" \/><\/span><\/span><\/li>\n<li>In the vector form, equation of a plane which is at a distance d from the origin, and <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?\\widehat n\" \/><\/span><\/span>is the unit vector normal to the plane through the origin is <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image035.png\" \/><\/li>\n<li>Equation of a plane which is at a distance of d from the origin and the direction cosines of the normal to the plane as l, m, n is <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image036.png\" \/>.<\/li>\n<li>The equation of a plane through a point whose position vector is a and perpendicular to the vector <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?\\overrightarrow {\\rm{N}}\" \/><\/span><\/span>\u00a0is <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( {\\overrightarrow r - \\overrightarrow a } \\right).\\overrightarrow {\\rm{N}} = 0\" \/><\/span><\/span>.<\/li>\n<li>Equation of a plane perpendicular to a given line with direction ratios A, B, C and passing through a given point <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image017.png\" \/>is <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image038.png\" \/><\/li>\n<li>Equation of a plane passing through three non collinear points <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image017.png\" \/>,\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image039.png\" \/>\u00a0\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image040.png\" \/><\/li>\n<li>Vector equation of a plane that contains three non collinear points having position vectors <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?\\overrightarrow a ,\\overrightarrow b\" \/><\/span><\/span>and <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?\\overrightarrow c\" \/><\/span><\/span>\u00a0is \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?\\left( {\\overrightarrow r - \\overrightarrow a } \\right).\\left[ {\\left( {\\overrightarrow b - \\overrightarrow a } \\right) \\times \\left( {\\overrightarrow c - \\overrightarrow a } \\right)} \\right] = 0\" \/><\/span><\/span>.<\/li>\n<li>Equation of a plane that cuts the coordinates axes at <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image043.png\" \/>\u00a0is <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image044.png\" \/>.<\/li>\n<li>Vector equation of a plane that passes through the intersection of planes <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?\\overrightarrow r .\\overrightarrow {{n_1}} = {d_1}\" \/><\/span><\/span>\u00a0and <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?\\overrightarrow r .\\overrightarrow {{n_2}} = {d_2}\" \/><\/span><\/span>\u00a0is\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?\\overrightarrow r \\left( {\\overrightarrow {{n_1}} - \\lambda \\overrightarrow {{n_2}} } \\right) = {d_1} + \\lambda {d_2}\" \/><\/span><\/span>, \u00a0where <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image047.png\" \/>\u00a0is any non-zero constant.<\/li>\n<li>Cartesian equation of a plane that passes that passes through the intersection of two given planes <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image048.png\" \/>\u00a0and <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image049.png\" \/>is<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image050.png\" \/><\/li>\n<li>Two lines <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?\\overrightarrow r = \\overrightarrow {{a_1}} + \\lambda \\overrightarrow {{b_1}}\" \/><\/span><\/span>\u00a0and <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?\\overrightarrow r = \\overrightarrow {{a_2}} + \\mu \\overrightarrow {{b_2}}\" \/><\/span><\/span>\u00a0are coplanar if <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( {\\overrightarrow {{a_2}} - \\overrightarrow {{a_1}} } \\right).\\left( {\\overrightarrow {{b_1}} \\times \\overrightarrow {{b_2}} } \\right) = 0.\" \/><\/span><\/span><\/li>\n<li>Two planes <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?{a_1}x + {b_1}y + {c_1}z + {d_1} = 0\" \/><\/span><\/span>\u00a0and <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?{a_2}x + {b_2}y + {c_2}z + {d_2} = 0\" \/><\/span><\/span>\u00a0 \u00a0are coplanar if \u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image056.png\" \/><\/li>\n<li>In the vector form, if <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image013.png\" \/>\u00a0is the angle between the two planes, <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?\\overrightarrow r .\\overrightarrow {{n_1}} = {d_1}\" \/><\/span><\/span>\u00a0and <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?\\overrightarrow r .\\overrightarrow {{n_2}} = {d_2}\" \/><\/span><\/span>, then <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?\\theta = {\\cos ^{ - 1}}\\left| {{{\\overrightarrow {{n_1}} .\\overrightarrow {{n_2}} } \\over {\\overrightarrow {{n_1}} \\left| {\\overrightarrow {{n_2}} } \\right|}}} \\right|\" \/><\/span><\/span><\/li>\n<li>The angle <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image060.png\" \/>\u00a0between the line <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?\\overrightarrow r = \\overrightarrow a + \\lambda \\overrightarrow b\" \/><\/span><\/span>\u00a0and the plane <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?\\overrightarrow r .\\widehat n = d\" \/><\/span><\/span>\u00a0is\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?\\sin \\phi = {{\\overrightarrow b .\\widehat n} \\over {\\left| {\\overrightarrow b } \\right|\\left| {\\widehat n} \\right|}}\" \/><\/span><\/span><\/li>\n<li>The angle <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image013.png\" \/>\u00a0between the planes <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image048.png\" \/>\u00a0and <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image049.png\" \/>\u00a0is given by <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image064.png\" \/><\/li>\n<li>The distance of a point whose position vector is <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?\\overrightarrow a\" \/><\/span><\/span>\u00a0from the plane <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?\\overrightarrow r .\\widehat n = d\" \/><\/span><\/span>\u00a0 is <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| {d - \\overrightarrow a .\\widehat n} \\right|\" \/><\/span><\/span>.<\/li>\n<li>The distance from a point <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image068.png\" \/>\u00a0to the plane Ax + By + Cz + D = 0 is <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch11\/image069.png\" \/><\/li>\n<li>Equation of any plane that is parallel to a plane that is parallel to a plane Ax + By + Cz + D = 0 is Ax + By + Cz + k = 0, where k is a different constant other than D.<strong>\u00a0 \u00a0 \u00a0\u00a0<\/strong><\/li>\n<\/ul>\n<h2><strong>CBSE Class 12 Revision Notes and Key Points<\/strong><\/h2>\n<p>Three Dimensional Geometry class 12 Notes Mathematics. CBSE quick revision note for class-12 Chemistry Physics Maths, 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-12-physics\/1251\/cbse-revision-notes\/7\/\">Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-chemistry\/1267\/cbse-revision-notes\/7\/\">Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-revision-notes\/7\/\">Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-biology\/1298\/cbse-revision-notes\/7\/\">Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-accountancy\/1315\/cbse-revision-notes\/7\/\">Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-economics\/1327\/cbse-revision-notes\/7\/\">Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-business-studies\/1727\/cbse-revision-notes\/7\/\">Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-computer-science\/1851\/cbse-revision-notes\/7\/\">Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-informatics-practices\/1873\/cbse-revision-notes\/7\/\">Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-english-core\/1855\/cbse-revision-notes\/7\/\">English Core<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-history\/1869\/cbse-revision-notes\/7\/\">History<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physical-education\/1877\/cbse-revision-notes\/7\/\">Physical Education<\/a><\/li>\n<\/ul>\n<p>To download Three Dimensional Geometry class 12 Notes Mathematics, sample paper for class 12 Physics, Chemistry, 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 Three Dimensional Geometry, NCERT Exemplar Three Dimensional Geometry, 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<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/relations-functions-class-12-notes-mathematics\/\">Relations and Functions class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/inverse-trigonometric-functions-class-12-notes-mathematics\/\">Inverse Trigonometric Functions class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/matrices-class-12-notes-mathematics\/\">Matrices class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/determinants-class-12-notes-mathematics\/\">Determinants class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/continuity-differentiability-class-12-notes-mathematics\/\">Continuity and Differentiability class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/application-derivatives-class-12-notes-mathematics\/\">Application of Derivatives class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/integrals-class-12-notes-mathematics\/\">Integrals class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/application-integrals-class-12-notes-mathematics\/\">Application of Integrals class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/differential-equations-class-12-notes-mathematics\/\">Differential Equations class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/vector-algebra-class-12-notes-mathematics\/\">Vector Algebra class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/linear-programming-class-12-notes-mathematics\/\">Linear Programming class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/probability-class-12-notes-mathematics\/\">Probability class 12 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Three Dimensional Geometry Class 12 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Three Dimensional Geometry class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school-based annual examinations. Class 12 Mathematics notes on chapter 11 Three &#8230; <a title=\"Three Dimensional Geometry Class 12 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/three-dimensional-geometry-class-12-notes-mathematics\/\" aria-label=\"More on Three Dimensional Geometry Class 12 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":9266,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[48,456],"tags":[457,150,461,426,240,575],"class_list":["post-9350","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-12","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-mathematics-notes","tag-quick-revision","tag-quick-revision-notes","tag-three-dimensional-geometry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Three Dimensional Geometry Class 12 Notes Mathematics<\/title>\n<meta name=\"description\" content=\"Three Dimensional Geometry class 12 Notes Mathematics chapter 11 in PDF format for free download. 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