Relative to the origin $O$, the position vectors of the points $A$, $B$ and $C$ are $\overrightarrow{OA}=\begin{pmatrix}2\\1\\-3\end{pmatrix}$, $\overrightarrow{OB}=\begin{pmatrix}0\\4\\1\end{pmatrix}$ and $\overrightarrow{OC}=\begin{pmatrix}-3\\-2\\2\end{pmatrix}$.
(a)[2]
Point $D$ is defined so that $ABCD$ forms a trapezium and $\overrightarrow{DC}=3\overrightarrow{AB}$. Determine the position vector of $D$.
(b)[5]
The trapezium's diagonals meet at the point $P$. Determine the position vector of $P$.
(c)[4]
Use a scalar product to find angle $ABC$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply a correct method to determine $\vec{OD}$” …