If a line makes angles $90^\circ$, $60^\circ$ and $30^\circ$ with the positive direction of $x$, $y$ and $z$-axis respectively, find its direction cosines.

$(0, \frac{1}{2}, \frac{\sqrt{3}}{2})$

The correct answer is Option (2) → $(0, \frac{1}{2}, \frac{\sqrt{3}}{2})$ ##

Let the d.c.'s of the lines be $l$, $m$, $n$. Then

$l = \cos 90^\circ = 0, \quad m = \cos 60^\circ = \frac{1}{2}, \quad n = \cos 30^\circ = \frac{\sqrt{3}}{2}$.