(i)[4]
Show that angle $ABC$ equals $90^{\circ}$.
(ii)[3]
Find the area of triangle $ABC$, and give your answer correct to $1$ decimal place.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking $O$ as the origin, the position vectors of the points $A$, $B$ and $C$ are $overrightarrow{OA} = \begin{pmatrix} 3 \\ 2 \\ -3 \end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix} 5 \\ -1 \\ -2 \end{pmatrix}$ and $\overrightarrow{OC} = \begin{pmatrix} 6 \\ 1 \\ 2 \end{pmatrix}$.