Answer
$30^{\circ}$
Work Step by Step
The direction angle $\theta$ of vector $u=\left\langle a,b\right\rangle$ satisfies $\tan \theta =\frac{b}{a}$ where, $a\neq 0.$
Now $u=\left\langle a,b\right\rangle=\left\langle \sqrt 3,1\right\rangle$ implies $a=\sqrt 3~~ \text{and }~~b=1$.
Therefore, direction angle $\theta$ is $$\theta=\tan^{-1}\left( \frac{b}{a}\right)=\tan^{-1}\left( \frac{1}{\sqrt 3}\right)=30^{\circ}$$
Since the vector $u$ has both positive components, it lies in quadrant $I$.
Hence, the direction angle of vector $u$ is $30^{\circ}$.
