With respect to the origin O, the position vectors of the points A and B are given by \(\overrightarrow{OA} = \begin{pmatrix} 1 \\ 2 \\ -1 \end{pmatrix}\) and \(\overrightarrow{OB} = \begin{pmatrix} 0 \\ 3 \\ 1 \end{pmatrix}\).

(a) Find a vector equation for the line l through A and B.

(b) The point C lies on l and is such that \(\overrightarrow{AC} = 3\overrightarrow{AB}\). Find the position vector of C.

(c) Find the possible position vectors of the point P on l such that \(OP = \sqrt{14}\).