Question

If a line makes the angle $\alpha ,\beta ,\gamma$ with three dimensional coordinate axes respectively, then $\cos 2\alpha +\cos 2\beta +\cos 2\gamma$ is equal to

• A. $-2$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

Answer: (B)

$-1$

We need to find value of $\cos 2\alpha +\cos 2\beta +\cos 2\gamma$
It is further equal to ${\cos }^2\alpha -1+{\cos }^2\beta -1+{\cos }^2\gamma -1$
$=2({\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma )-3$
$=2\left(1\right)-3=2=-1(\because l^2+m^2+n^2=1)$