The diagram shows that $ADB$ and $ACF$ are straight lines. $BC$ meets $DF$ at $E$. The ratio $AC : CF = 2 : 1$. Also, $\overrightarrow{DB} = \mathbf{p}$, $\overrightarrow{BE} = 3\mathbf{q}$, $\overrightarrow{EC} = 2\mathbf{q}$ and $\overrightarrow{AC} = 3\mathbf{p} + 5\mathbf{q}$.
(a)[1]
Express $\overrightarrow{AB}$ using $\mathbf{p}$.
(b)[1]
Express $\overrightarrow{CF}$ using $\mathbf{p}$ and/or $\mathbf{q}$.
(c)[1]
Express $\overrightarrow{EF}$ using $\mathbf{p}$ and/or $\mathbf{q}$.
(d)[2]
Given $\overrightarrow{EF} = k\overrightarrow{DE}$, determine $k$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$3p$ ” …