Explanation

(b)
Given have magnitude of $\overrightarrow{\mathbf{OA}}$ and $\overrightarrow{\mathbf{OB}}\$ are 5 and 6 respectively
and $\angle BOA = 60{^\circ}$
$\therefore\ \overrightarrow{\mathbf{OA}} \bullet \overrightarrow{\mathbf{OB}} = \left| \overrightarrow{\mathbf{OA}} \right|\left| \overrightarrow{\mathbf{OB}} \right| \bullet \cos{60{^\circ}}$
$\Longrightarrow \ \overrightarrow{\mathbf{OA}} \bullet \overrightarrow{\mathbf{OB}} = 5 \bullet 6\cos{60{^\circ}}$
$\mathbf{\Longrightarrow}\overrightarrow{\mathbf{OA}} \bullet \overrightarrow{\mathbf{OB}} = 5 \times 6 \times \frac{1}{2} = 15$