13. Vectors
$$
a=(1, \sin \theta), b=(\cos \theta, \sqrt{3})(\theta \in \mathbf{R}) \text {. }
$$

Then the range of values for $|a-b|$ is $\qquad$ .
13. $[1,3]$.
$$
\begin{array}{l}
|a-b|=\sqrt{(1-\cos \theta)^{2}+(\sin \theta-\sqrt{3})^{2}} \\
=\sqrt{5-2(\cos \theta-\sqrt{3} \sin \theta)} \\
=\sqrt{5-4 \sin \left(\frac{\pi}{6}-\theta\right)} \in[1,3] .
\end{array}
$$