XII Maths Chapter 11 Three Dimensional Geometry | Page 2

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 )