If a line makes the angle , , with three dimensional co-ordinate … - Vidyadip

MCQ

If a line makes the angle $\alpha ,\beta ,\gamma $ with three dimensional co-ordinate axes respectively, then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = $

A
$-2$
✓
$-1$
C
$1$
D
$2$

✓

Answer

Correct option: B.

$-1$

b
(b) $\cos \,2\alpha + \cos \,2\beta + \cos \,2\gamma $

$ = 2\,{\cos ^2}\alpha - 1 + 2\,{\cos ^2}\beta - 1 + 2\,{\cos ^2}\gamma - 1$

$ = 2\,({\cos ^2}\alpha + {\cos ^2}\beta + {\cos ^2}\gamma ) - 3 = 2 - 3 = - 1.$

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