If a line makes angles \(\alpha, \beta\) and \(\gamma\) with the positive directions of coordinate axes respectively, then \(\cos 2\alpha + \cos 2\beta + \cos 2\gamma\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −1
The direction cosines of a line satisfy \(\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1\). Using \(\cos 2\theta = 2\cos^2\theta - 1\) for each angle:
\(\cos 2\alpha + \cos 2\beta + \cos 2\gamma = 2(\cos^2\alpha + \cos^2\beta + \cos^2\gamma) - 3\)
\(= 2(1) - 3 = -1\)