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. Direction cosines of a line are the cosines of the angles made by the line with the positive directions of the coordinate axes. Direction ratios of a line are the numbers which are proportional to the direction cosines of a line. Three Dimensional Geometry of Class 12 enables the students to understand the following:
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.