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

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

1. Find \(\overrightarrow{AC}\).
2. The point M is the mid-point of AC. Find the unit vector in the direction of \(\overrightarrow{OM}\).
3. Evaluate \(\overrightarrow{AB} \cdot \overrightarrow{AC}\) and hence find angle BAC.