(i)[3]
Find $\overrightarrow{AX}$ and prove that $AXB$ is a straight line.
(ii)[3]
Show that $CX$ meets $AX$ at right angles.
(iii)[3]
Determine the area of triangle $ABC$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Taking origin $O$ as the reference point, the position vectors of the points $A$, $B$ and $X$ are given by $\overrightarrow{OA} = \begin{pmatrix} -8 \\ -4 \\ 2 \end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix} 10 \\ 2 \\ 11 \end{pmatrix}$ and $\overrightarrow{OX} = \begin{pmatrix} -2 \\ -2 \\ 5 \end{pmatrix}$.