2018 TGM P1 Q6

With reference to the origin, the points \(A\) and \(B\) are such that \(\overrightarrow{OA}=\mathbf{a}\) and \(\overrightarrow{OB}=\mathbf{b}\). The points \(P\) and \(Q\) lie on \(AB\) and \(OB\) respectively such that \(AP:PB=1:3\) and \(OQ:QB=3:4\). The lines \(AQ\) and \(OP\) cross at \(R\). (see diagram)

Find

1. \(\overrightarrow{OR}\) in terms of \(\mathbf{a}\) and \(\mathbf{b}\),[6]
2. the ratio of \(AR:RQ\),[2]