If a line makes angles $α,β$ and $γ$ with the positive directions of coordinate axes respectively, then $\cos 2α + \cos 2β + \cos 2γ$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -1
Use the identity:
$\cos 2\alpha = 2\cos^{2}\alpha - 1$
So,
$\cos 2\alpha + \cos 2\beta + \cos 2\gamma$
$= 2(\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma) - 3$
For a line in 3-D, direction cosines satisfy:
$\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma = 1$
Therefore,
$\cos 2\alpha + \cos 2\beta + \cos 2\gamma = 2(1) - 3 = -1$
The value is $-1$.