(i)[6]
Determine the equation of $m$, and give your result in the form $ax + by + cz = d$.
(ii)[5]
Determine the length of the perpendicular drawn from $C$ to the line passing through $A$ and $B$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Taking the origin $O$ as the reference point, the position vectors of $A$, $B$ and $C$ are given by $\overrightarrow{OA} = \begin{pmatrix}3 \\ -2 \\ 4\end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix}2 \\ -1 \\ 7\end{pmatrix}$ and $\overrightarrow{OC} = \begin{pmatrix}1 \\ -5 \\ -3\end{pmatrix}$. The plane $m$ is parallel to $OC$ and passes through $A$ and $B$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Form equations by taking the scalar product of suitable vectors or by subtracting point equations” …
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