Introduction to Three Dimensional Geometry

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In 2D, we need two perpendicular axes (x and y) to locate a point in a plane. In 3D, we need three mutually perpendicular axes (x, y, and z) to locate a point in space. 2D uses ordered pairs (x,y) whi

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The three coordinate axes are: 1. X-axis (horizontal, left-right) 2. Y-axis (horizontal, front-back) 3. Z-axis (vertical, up-down) All three axes are mutually perpendicular to each other and intersec

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Coordinate planes are formed by pairs of coordinate axes. The three coordinate planes are: 1. XY-plane (formed by x and y axes) 2. YZ-plane (formed by y and z axes) 3. ZX-plane (formed by z and x axes

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Octants are the eight regions into which 3D space is divided by the three coordinate planes. There are exactly 8 octants, numbered I through VIII. They are named: XOYZ, X′OYZ, X′OY′Z, XOY′Z, XOYZ′, X′

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The coordinates of the origin O are (0, 0, 0). This is the point where all three coordinate axes intersect, and it serves as the reference point for the entire coordinate system.

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x, y, and z represent the perpendicular distances from the coordinate planes: - x = perpendicular distance from YZ-plane - y = perpendicular distance from ZX-plane - z = perpendicular distance from XY

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Any point on the x-axis has coordinates of the form (x, 0, 0), where x can be any real number. The y and z coordinates are zero because the point lies on the x-axis itself.

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Points on y-axis: (0, y, 0) where y can be any real number Points on z-axis: (0, 0, z) where z can be any real number In both cases, the coordinates corresponding to the other two axes are zero.