The position vectors of points A, B and C relative to an origin O are given by

\(\overrightarrow{OA} = \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} 6 \\ -1 \\ 7 \end{pmatrix} \quad \text{and} \quad \overrightarrow{OC} = \begin{pmatrix} 2 \\ 4 \\ 7 \end{pmatrix}.\)

(i) Show that angle \(BAC = \cos^{-1}\left(\frac{1}{3}\right).\)

(ii) Use the result in part (i) to find the exact value of the area of triangle \(ABC.\)