13 Vector $\vec{a}=(1, \sin \theta), \vec{b}=(\cos \theta, \sqrt{3}), \theta \in \mathbf{R}$, then the range of $|\vec{a}-\vec{b}|$ is $\qquad$ .
$13[1,3]$ Hint:
$$
\begin{aligned}
|\vec{a}-\vec{b}| & =\sqrt{(1-\cos \theta)^{2}+(\sin \theta-\sqrt{3})^{2}} \\
& =\sqrt{5-2(\cos \theta-\sqrt{3} \sin \theta)} \\
& =\sqrt{5-4 \sin \left(\frac{\pi}{6}-\theta\right)}
\end{aligned}
$$

Its maximum value is 3, minimum value is 1, and the range of values is $[1,3]$.