If the direction cosines of a variable line in two adjacent positions be and

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

If the direction cosines of a variable line in two adjacent positions be

l, m, n

and

l + \delta l, m + \delta m, n + \delta n

, show that the small angle

\delta\theta

between the two positions, is given by

\delta\theta^2 = \delta l^2 + \delta m^2 + \delta n^2