If a line makes angles $α,β,γ$ with the positive directions of x-axis, y-axis, z-axis respectively, then the value of $\cos 2α + \cos 2β+ \cos 2γ$ is equal to

-1

The correct answer is Option (2) → -1

Let $l=\cos\alpha,\; m=\cos\beta,\; n=\cos\gamma$ be the direction cosines.

Property: $l^{2}+m^{2}+n^{2}=1$.

Use identity $\cos 2\theta=2\cos^{2}\theta-1$.

$\cos2\alpha+\cos2\beta+\cos2\gamma=2(l^{2}+m^{2}+n^{2})-3$

$=2(1)-3$

$=-1$

Final answer: $-1$