(a) Vectors \(\mathbf a\), \(\mathbf b\) and \(\mathbf c\) are such that

\(\mathbf a=\binom{5}{-6},\qquad \mathbf b=\binom{11}{-15},\qquad 3\mathbf a+\mathbf c=\mathbf b.\)

(i) Find \(\mathbf c\).

(ii) Find the unit vector in the direction of \(\mathbf b\).

(b) In the diagram, \(\overrightarrow{OP}=\mathbf p\) and \(\overrightarrow{OQ}=\mathbf q\). The point \(R\) lies on \(PQ\) such that \(PR=3RQ\).

Find \(\overrightarrow{OR}\) in terms of \(\mathbf p\) and \(\mathbf q\), simplifying your answer.