{"id":126086,"date":"2023-02-13T10:25:34","date_gmt":"2023-02-13T04:55:34","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=126086"},"modified":"2024-12-09T12:38:20","modified_gmt":"2024-12-09T07:08:20","slug":"study-materials-cbse-notes-maths-3d-geometry-introduction-coordinate-system-and-formulas","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/","title":{"rendered":"Introduction To 3D Geometry, Coordinate System and Formulas"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/#Introduction_to_3-Dimensional_Geometry\" title=\"Introduction to 3-Dimensional Geometry\">Introduction to 3-Dimensional Geometry<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/#Coordinate_System_in_3D_Geometry\" title=\"Coordinate System in 3D Geometry\">Coordinate System in 3D Geometry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/#The_Properties_of_Three-dimensional_Space\" title=\"The Properties of Three-dimensional Space:\">The Properties of Three-dimensional Space:<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/#Rectangular_Coordinate_System_in_Space\" title=\"Rectangular Coordinate System in Space\">Rectangular Coordinate System in Space<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/#Coordinates_of_a_Point_in_Space\" title=\"Coordinates of a Point in Space\">Coordinates of a Point in Space<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/#Perpendicular_Distance_of_a_Point_from_a_Line\" title=\"Perpendicular Distance of a Point from a Line\">Perpendicular Distance of a Point from a Line<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/3d-geometry\/introduction-coordinate-system-and-formulas\/#Difference_between_2D_Shape_and_3D_Geometric_Shape\" title=\"Difference between 2D Shape and 3D Geometric Shape\">Difference between 2D Shape and 3D Geometric Shape<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span style=\"color: #0000ff; font-size: 14pt;\"><strong>Introduction To 3D Geometry<\/strong><\/span><\/p>\n<p>A three-dimensional geometry is a branch of mathematics that studies the properties of shapes in three dimensions. It is an extension of two-dimensional geometry, which studies shapes in two dimensions. Just as in two dimensions, shapes in three dimensions can be classified according to their properties.<\/p>\n<p>There are three basic types of shapes in three dimensions: points, lines, and planes. Points are the simplest shapes, and they have no dimensions. Lines are one-dimensional shapes, and they are defined<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-126083 size-medium\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/Introduction-To-3D-Geometry-300x212.jpg\" alt=\"Introduction- 3D Geometry\" width=\"300\" height=\"212\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/Introduction-To-3D-Geometry-300x212.jpg?v=1645814675 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/Introduction-To-3D-Geometry.jpg?v=1645814675 606w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_3-Dimensional_Geometry\"><\/span><span style=\"color: #0000ff; font-size: 14pt;\">Introduction to 3-Dimensional Geometry<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>3-dimensional geometry is the study of shapes in three dimensions. These shapes can be points, lines, planes, and solids. In 3-dimensional geometry, we use three coordinates to describe the location of a point in space. The three coordinates are x, y, and z.<\/p>\n<p>The most basic shapes in 3-dimensional geometry are points, lines, and planes. A point is a location in space with no dimensions. A line is a location in space with one dimension<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Coordinate_System_in_3D_Geometry\"><\/span><span style=\"color: #0000ff;\">Coordinate System in 3D Geometry<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A coordinate system is a way of representing points in space using numbers. In a three-dimensional coordinate system, points are represented by three numbers, called coordinates. The first coordinate is the distance from the origin in the x-direction. The second coordinate is the distance from the origin in the y-direction. The third coordinate is the distance from the origin in the z-direction. The origin is the point at (0,0,0).<\/p>\n<p>Here is an example of a<\/p>\n<h3><span class=\"ez-toc-section\" id=\"The_Properties_of_Three-dimensional_Space\"><\/span><span style=\"color: #0000ff;\">The Properties of Three-dimensional Space:<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In mathematics, three-dimensional space is a geometric setting with three dimensions. It is the natural setting for most physical objects and phenomena. All the objects we experience in our everyday lives exist in three-dimensional space. This space is commonly represented in mathematical models by three coordinate axes (x, y, and z) that intersect at the origin. Points in three-dimensional space are usually described by a triplet of real numbers, (x, y, z).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Rectangular_Coordinate_System_in_Space\"><\/span><span style=\"color: #0000ff; font-size: 14pt;\">Rectangular Coordinate System in Space<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A rectangular coordinate system is a coordinate system that uses perpendicular lines called axes to identify points in a plane or in space. The axes are usually labeled x and y, or east-west and north-south. The point where the axes intersect is called the origin.<\/p>\n<p>Points in a plane can be identified by their distance from the origin and their direction. Points in space can be identified by their distance from the origin, their direction, and their altitude.<\/p>\n<p>The coordinate system can<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Coordinates_of_a_Point_in_Space\"><\/span><span style=\"font-size: 14pt; color: #0000ff;\">Coordinates of a Point in Space<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A point in space can be located by its coordinates. A coordinate is a number that uniquely identifies a point in space. The coordinate system is based on a set of axes that are perpendicular to each other. The x-axis is horizontal and the y-axis is vertical. The z-axis is perpendicular to the x- and y-axes and extends out of the page.<\/p>\n<p>The coordinate of a point can be written as (x, y, z). The x-<\/p>\n<p><span style=\"color: #0000ff; font-size: 14pt;\"><strong>Some Key Points to Remember<\/strong><\/span><\/p>\n<p>About the Holocaust<\/p>\n<p>Some key points to remember about the Holocaust are:<\/p>\n<p>1. The Holocaust was a genocide in which Nazi Germany killed six million Jews.<\/p>\n<p>2. The Holocaust was the result of a long and systematic process of demonization of the Jews by the Nazis.<\/p>\n<p>3. The Nazis used a variety of means to kill the Jews, including mass shootings, gas chambers, and concentration camps.<\/p>\n<p>4. The Holocaust was one of the worst atrocities in human history<\/p>\n<p><strong><span style=\"font-size: 14pt; color: #0000ff;\">Direction Cosines of a Line<\/span><\/strong><\/p>\n<p>In mathematics, direction cosines are used to represent the direction of a vector in three-dimensional space. A vector is represented as an arrow with a certain length and a certain direction. The direction of the vector is given by its direction cosines.<\/p>\n<p>There are three direction cosines, one for each dimension. The direction cosine for the x-axis is the cosine of the angle between the vector and the x-axis. The direction cosine for the y-axis<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Perpendicular_Distance_of_a_Point_from_a_Line\"><\/span><span style=\"font-size: 14pt; color: #0000ff;\">Perpendicular Distance of a Point from a Line<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A point is said to be perpendicular to a line if it is at a right angle to the line. The distance of a point from a line is the length of the line segment from the point to the line. The perpendicular distance of a point from a line is the length of the line segment from the point to the line at a right angle to the line.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Difference_between_2D_Shape_and_3D_Geometric_Shape\"><\/span><span style=\"color: #0000ff;\">Difference between 2D Shape and 3D Geometric Shape<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A 2D geometric shape is a shape that has two dimensions- width and length. A 3D geometric shape is a shape that has three dimensions- width, length, and height.<\/p>\n<p>2D shapes can be flat or curved. 3D shapes can be curved, but they can also be solid, like a ball or a cube.<\/p>\n<p>2D shapes can be drawn on a piece of paper. 3D shapes can be made out of materials like wood, metal,<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction To 3D Geometry A three-dimensional geometry is a branch of mathematics that studies the properties of shapes in three [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Introduction To 3D Geometry","_yoast_wpseo_title":"Notes for Introduction To 3D Geometry, Coordinate System and Formulas","_yoast_wpseo_metadesc":"Introduction To 3D Geometry is a branch of mathematics that studies the properties of shapes in three 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