If a line makes angles 90°, 60° and $θ$ with x, y and z axis respectively, where $θ$ is acute, then value of $θ$ is:

$\frac{π}{6}$ $\frac{π}{4}$ $\frac{π}{3}$ $\frac{π}{2}$

$\frac{π}{6}$

$l=\cos 90°$, $m=\cos 60°$, $n=\cos θ$ so these are direction cosines $l^2+m^2+n^2=1⇒\cos^2 90°+\cos^2 60°+\cos^2 θ=1$ so $0+\frac{1}{4}+\cos^2 θ=1$ $\cos^2 θ=\frac{3}{4}⇒\cos^2 θ=\frac{\sqrt{3}}{2}$ $⇒θ=30°=\frac{π}{6}$