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11. three dimension geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths11. three dimension geometry1 Mark
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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