Prove that the two lines whose direction cosines are connected by the two relations…

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

Problem

Prove that the two lines whose direction cosines are connected by the two relations

al + bm + cn = 0

and

ul^2 + vm^2 + wn^2 = 0

are perpendicular if

a^2(v + w) + b^2(w + u) + c^2(u + v) = 0

and parallel if

\frac{a^2}{u} + \frac{b^2}{v} + \frac{c^2}{w} = 0