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
Answer & explanation
Correct answer: option 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 $2$.