2. The circumcenter of $\triangle A B C$ is $O, A B=2, A C=3, B C=\sqrt{7}$, then $\overrightarrow{O A} \cdot \overrightarrow{B C}$ equals
$$
\overrightarrow{A O} \cdot \overrightarrow{C B}=\overrightarrow{A O} \cdot(\overrightarrow{A B}-\overrightarrow{A C})=\frac{1}{2}\left(\overrightarrow{A B}^{2}-\overrightarrow{A C}^{2}\right)=-\frac{5}{2}
$$