A line is perpendicular to the $x$-axis, makes an angle of $\frac{5\pi}{6}$ with the $y$-axis and an acute angle with the $z$-axis. What are its direction cosines?

Explanation

1. 01

   Perpendicular to the $x$-axis: $l = \cos\frac{\pi}{2} = 0$; and $m = \cos\frac{5\pi}{6} = -\frac{\sqrt{3}}{2}$.

2. 02

   $n^{2} = 1 - 0 - \frac{3}{4} = \frac{1}{4}$, and the acute angle gives $n = \frac{1}{2}$.