With respect to the origin O, the points A, B, C and D have position vectors given by

\(\overrightarrow{OA} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} 1 \\ 2 \\ -3 \end{pmatrix}, \quad \overrightarrow{OC} = \begin{pmatrix} 1 \\ -2 \\ 5 \end{pmatrix} \quad \text{and} \quad \overrightarrow{OD} = \begin{pmatrix} 5 \\ -6 \\ 11 \end{pmatrix}.\)

(a) Find the obtuse angle between the vectors \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\).

The line \(l\) passes through the points \(A\) and \(B\).

(b) Find a vector equation for the line \(l\).

(c) Find the position vector of the point of intersection of the line \(l\) and the line passing through \(C\) and \(D\).