Answer
$108.44^{\circ}$
Work Step by Step
Let us consider that a vector $v$ is given by $v=pi+qj$ and makes an angle of $\alpha$ with the positive $x$-axis. The direction angle $\alpha$ for the given vector can be determined using the formula:
$\tan \alpha=\dfrac{q}{p}$
Here, we have: $v=-i +3j $
Now, $\tan \alpha=\dfrac{ 3}{-1}=-3$
Since the angle must be in quadrant II, the direction angle is:
$\alpha=\arctan (-3) \approx 108.44^{\circ}$
