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

-1

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 $-1$.