A vector has direction ratios $1, -2, 2$ and makes an obtuse angle with the $x$-axis. What are its direction cosines?

Explanation

1. 01

   $\sqrt{1 + 4 + 4} = 3$, so the direction cosines are $\pm\left(\frac{1}{3}, -\frac{2}{3}, \frac{2}{3}\right)$.

2. 02

   An obtuse angle with the $x$-axis needs $l < 0$: take the minus sign, $-\frac{1}{3}, \frac{2}{3}, -\frac{2}{3}$.