Question 82, Given vectors $\overrightarrow{\mathrm{OA}}$ and $\overrightarrow{\mathrm{OB}}$ have an angle of $120^{\circ}$ between them, $|\overrightarrow{\mathrm{OA}}|=2|\overrightarrow{\mathrm{OB}}|=6$. A line segment $\mathrm{PQ}$ of length $2|\overrightarrow{\mathrm{AB}}|$ is drawn through 0, and $\mathrm{P}, \mathrm{Q}$ are symmetric about 0. When the angle between vector $\overrightarrow{\mathrm{PQ}}$ and $\overrightarrow{\mathrm{AB}}$ is what, will $\overrightarrow{\mathrm{AP}} \cdot \overrightarrow{\mathrm{BQ}}$ be maximized, and find this maximum value.