The diagram shows a triangle \(OAB\). The point \(P\) is the midpoint of \(OA\) and the point \(Q\) lies on \(OB\) such that \(\overrightarrow{OQ}=\dfrac14\overrightarrow{OB}\). The position vectors of \(P\) and \(Q\) relative to \(O\) are \(\mathbf{p}\) and \(\mathbf{q}\) respectively.

(i) Find, in terms of \(\mathbf{p}\) and \(\mathbf{q}\), an expression for each of the vectors \(\overrightarrow{PQ}\), \(\overrightarrow{QA}\) and \(\overrightarrow{PB}\).

(ii) Given that \(\overrightarrow{PR}=\lambda\overrightarrow{PB}\) and that \(\overrightarrow{QR}=\mu\overrightarrow{QA}\), find an expression for \(\overrightarrow{PQ}\) in terms of \(\lambda\), \(\mu\), \(\mathbf{p}\) and \(\mathbf{q}\).

(iii) Using your expressions for \(\overrightarrow{PQ}\), find the value of \(\lambda\) and of \(\mu\).