Three Dimensional Geometry

RECTANGULAR COORDINATE SYSTEM IN SPACE

Let ‘O’ be any point in space and X’OX , Y’OY and Z’OZ be three lines perpendicular to each other. These lines are known as coordinate axes and O is called origin. The planes XY, YZ, ZX are known as the coordinate planes.

Coordinates of a Point in Space:

Consider a point P in space whose position is given by triad (x, y, z) where x, y, z are perpendicular distance from YZ-plane, ZX-plane and XY-plane respectively.

If we assume unit vectors along OX, OY, OZ respectively, then position vector of point P is or simply (x, y, z).

Note: Any point on –

⊠ x-axis = {( x, y, z) | y = z = 0}

⊠ y-axis = {(x, y, z) | x = z = 0}

⊠ z-axis = {(x, y, z) | x = y = 0}

⊠ xy plane = {(x, y, z) | z = 0}

⊠ yz plane = {(x, y, z) | x = 0}

⊠ zx plane = {(x, y, z) | y = 0}

⊠ OP = √(x2+y2+z2)

⊠ The three co-ordinate planes divide the whole space in eight compartments which are known as eight octants and since each of the coordinates of a point may be positive or negative, there are 23 (= 8) points whose coordinates have the same numerical values and which lie in eight octants, one in each.

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