(a)[2]
Find a vector equation that represents $m$.
(b)[4]
Find the position vector of the point where $m$ intersects the line passing through $C$ and $D$.
(c)[4]
Find the position vector of the point where the perpendicular from $C$ meets $m$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Relative to the origin $O$, the position vectors of the points $A$, $B$, $C$ and $D$ are given by $\overrightarrow{OA}=\begin{pmatrix}1\\5\\3\end{pmatrix}$, $\overrightarrow{OB}=\begin{pmatrix}0\\4\\1\end{pmatrix}$, $\overrightarrow{OC}=\begin{pmatrix}1\\-3\\1\end{pmatrix}$ and $\overrightarrow{OD}=\begin{pmatrix}3\\-5\\4\end{pmatrix}$. The line $m$ goes through the points $A$ and $B$.