(i)[3]
Prove that $AB$ is perpendicular to $BC$.
(ii)[3]
Prove that $ABCD$ is a trapezium.
(iii)[3]
Determine the area of $ABCD$, giving your answer correct to $2$ decimal places.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Using origin $O$ as the reference point, the position vectors of points $A$, $B$, $C$ and $D$, as displayed in the diagram, are $\vec{OA} = \begin{pmatrix}-1\\3\\-4\end{pmatrix}$, $\vec{OB} = \begin{pmatrix}2\\-3\\5\end{pmatrix}$, $\vec{OC} = \begin{pmatrix}4\\-2\\5\end{pmatrix}$ and $\vec{OD} = \begin{pmatrix}2\\2\\-1\end{pmatrix}$.