Coordinate System
The three mutually perpendicular lines in a space which divides the space into eight parts and if these perpendicular lines are the coordinate axes, then it is said to be a coordinate system.
Sign Convention
Distance between Two Points
Let P( x1, y1, z1) and Q( x2, y2, z2) be two given points. The distance between these points is given by
PQ √( x2 – x1) 2 +( y2 – y1) 2 +( z2 – z1) 2 The distance of a point P( x, y, z) from origin O is
OP = √x 2 + y 2 + z 2
Section Formulae
( i) The coordinates of any point, which divides the join of points P( x1, y1, z1) and Q( x2, y2, z2) in the ratio m: n internally are
( mx2 + nx1 / m + n, my2 + ny1 / m + n, mz2 + nz1 / m + n)