Three Dimensional Geometry

Direction cosines are the cosines

Direction cosines are the cosines of the angles made by a directed line with the positive x-, y-, and z-axes. They are written as l, m, n and satisfy

Any three numbers proportional to

Any three numbers proportional to the direction cosines of a line are called its direction ratios. If l, m, n are direction cosines and a, b, c are di

If

If a, b, c are direction ratios, then the direction cosines are l = ± a/√(a^2+b^2+c^2), m = ± b/√(a^2+b^2+c^2), n = ± c/√(a^2+b^2+c^2). The sign is ch

A unique line passes through two

A unique line passes through two given points P(x1,y1,z1) and Q(x2,y2,z2). Its direction ratios can be taken as x2-x1, y2-y1, z2-z1 or the reversed se

A line is uniquely determined if

A line is uniquely determined if it passes through a given point and has a given direction, or if it passes through two given points. If it passes thr