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
Answer & explanation
Correct answer: option 2
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: $-1$