With respect to the origin \(O\), the points \(A\) and \(B\) have position vectors given by \(\overrightarrow{OA} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}\) and \(\overrightarrow{OB} = \begin{pmatrix} 3 \\ 1 \\ -2 \end{pmatrix}\). The line \(l\) has equation \(\mathbf{r} = \begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ -2 \\ 1 \end{pmatrix}\).

(a) Find the acute angle between the directions of \(AB\) and \(l\).

(b) Find the position vector of the point \(P\) on \(l\) such that \(AP = BP\).