In the sketch, $B$ lies at the midpoint of $OD$, and the ratio $OA : AC = 1 : 3$. Also, $\overrightarrow{OA} = \vec{a}$ and $\overrightarrow{OB} = \vec{b}$.
(a(i))[1]
Express $\overrightarrow{OC}$ in the simplest form possible, using $\vec{a}$ and/or $\vec{b}$.
(a(ii))[1]
Express the vector $\overrightarrow{CD}$.
(b(i))[2]
Point $P$ is on $CD$ with $CP = \frac{3}{4}CD$. Express $\overrightarrow{AP}$ as simply as possible in terms of $\vec{a}$ and/or $\vec{b}$.
(b(ii))[1]
Find the ratio $AP : BD$.
(b(iii))[1]
What special kind of quadrilateral is $ABDP$?
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Thus, $4a$.” …