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

2

The correct answer is Option (2) → 2

Let the direction cosines of the line be

$l=\cos\alpha,\; m=\cos\beta,\; n=\cos\gamma$

Property of direction cosines

$l^2+m^2+n^2=1$

$\sin^2\alpha=1-\cos^2\alpha,\; \sin^2\beta=1-\cos^2\beta,\; \sin^2\gamma=1-\cos^2\gamma$

$\sin^2\alpha+\sin^2\beta+\sin^2\gamma =3-(\cos^2\alpha+\cos^2\beta+\cos^2\gamma)$

$=3-1$

$=2$

The value of $\sin^2\alpha+\sin^2\beta+\sin^2\gamma$ is $2$.