The position vectors of points $P$ and $Q$ relative to an origin $O$ are $\mathbf{p} = \mathbf{i} + 2\mathbf{j} - \mathbf{k}$ and $\mathbf{q} = 3\mathbf{i} - \mathbf{j} + 2\mathbf{k}$. (a) Find the vector $\overrightarrow{QP}$ and the distance $|PQ|$. (5 marks) (b) Show that angle $POQ$ is obtuse. (4 marks) (c) Find the value of $\lambda$ for which the vector $\mathbf{p} + \lambda\mathbf{q}$ is perpendicular to $\mathbf{q}$. (6 marks)