Three Dimensional Geometry

Direction cosines (d.c.’s) of a line: d.c.’s of a line are the cosines of angles made by the line with the positive direction of the coordinate axes. If l, m, and n are the d.c.’s of a line, then l2 + m2 + n2 = 1 d.c.’s of a line joining two points P (x1, y1, z1) and Q (x2, y2, z2) are , where PQ = Direction ratios (d.r.’s) of a line: d.r.’s of a line are the numbers which are proportional to the d.c.’s of the line. d.r.’s of a line joining two points P (x1, y1, z1) and Q (x2, y2, z2) are given by x1 –x2, y1 – y2, z1 – z2 or x2 – x1, y2 – y…