From the diagram, $A$ lies midway along $OC$, and $B$ is the point on $OD$ for which $OB = \dfrac{1}{3}OD$. Also, $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$.
(a(i))[1]
Write $\overrightarrow{AB}$ in the simplest possible form using $\mathbf{a}$ and $\mathbf{b}$.
(a(ii))[1]
Write $\overrightarrow{CD}$ in the simplest possible form in terms of $\mathbf{a}$ and $\mathbf{b}$.
(b(i))[2]
Point $E$ lies on $CD$ with $CE : ED = 1 : 2$. Write $\overrightarrow{BE}$ in the simplest possible form in terms of $\mathbf{a}$ and/or $\mathbf{b}$.
(b(ii))[1]
What special kind of quadrilateral does $ABEC$ form?
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$(-a+b)$” …