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

\(\overrightarrow{OA} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k}, \quad \overrightarrow{OB} = 2\mathbf{i} + 4\mathbf{j} + \mathbf{k}, \quad \text{and} \quad \overrightarrow{OC} = 3\mathbf{i} + 5\mathbf{j} - 3\mathbf{k}.\)

1. Find the exact value of the cosine of angle BAC.
2. Hence find the exact value of the area of triangle ABC.