$OACB$ forms a parallelogram. $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$. $P$ and $Q$ are points on $OC$ such that $OP = PQ = QC$.
(a(i))[1]
In terms of $\mathbf{a}$ and $\mathbf{b}$, write $\overrightarrow{OP}$ in its simplest form.
(a(ii))[1]
In terms of $\mathbf{a}$ and $\mathbf{b}$, express $\overrightarrow{BP}$ in the simplest possible form.
(b)[2]
Prove that triangles $OAQ$ and $CBP$ are congruent.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\frac{a+b}{3}$ or $\frac{a}{3}+\frac{b}{3}$” …