Answer
$333.43^{\circ}$
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=4 i -2j $
Now, $\tan \alpha=\dfrac{ -2}{4}=-0.5$
Since the angle must be in the quadrant IV, then the direction angle is: $\alpha=\arctan (-0.5)=333.43^{\circ}$
