In triangle $ACD$, $B$ lies at the midpoint of $AC$, and $E$ lies at the midpoint of $AD$. $\overrightarrow{AB}=6\mathbf{a}+3\mathbf{b}$ and $\overrightarrow{DC}=5\mathbf{a}+2\mathbf{b}$.
(a(i))[1]
Find $\overrightarrow{AC}$ in its simplest form, using $\mathbf{a}$ and $\mathbf{b}$.
(a(ii))[2]
Find $\overrightarrow{AD}$ in the simplest form, in terms of $\mathbf{a}$ and $\mathbf{b}$.
(b)[3]
Show that $\overrightarrow{EB}$ is parallel with $\overrightarrow{DC}$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Final answer: $12a+6b$ or $6(2a+b)$” …