Three Dimensional Geometry — Class 12 Mathematics

This chapter extends coordinate geometry to three dimensions, describing lines and planes vectorially and in Cartesian form. A line is given by , where is a point on it and its direction; in Cartesian form this is . The angle between two lines comes from the dot product of their direction vectors. A plane is written as , where is the unit normal, or in Cartesian form . The chapter computes the angle between two planes, between a line and a plane, and the shortest distance between two skew lines. These results give a complete algebraic description of position and orientation in space.