Relative to the origin O, the points A, B and C have position vectors given by

\(\overrightarrow{OA} = \begin{pmatrix} 1 \\ 3 \\ 1 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} 3 \\ 1 \\ 2 \end{pmatrix} \quad \text{and} \quad \overrightarrow{OC} = \begin{pmatrix} 5 \\ 3 \\ -2 \end{pmatrix}.\)

(a) Using a scalar product, find the cosine of angle BAC.

(b) Hence find the area of triangle ABC. Give your answer in a simplified exact form.