Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

With origin $O$, the position vectors of the points $A$, $B$ and $C$ are $\overrightarrow{OA} = \begin{pmatrix}3\\-2\\4\end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix}2\\-1\\7\end{pmatrix}$ and $\overrightarrow{OC} = \begin{pmatrix}1\\-5\\-3\end{pmatrix}$. The plane $m$ is parallel to $OC$ and passes through $A$ and $B$.
(a(i))[6]

Find the equation of $m$, and express it in the form $ax + by + cz = d$.

(a(ii))[5]

Find the length of the perpendicular from $C$ to the line joining $A$ and $B$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Construct the correct vector equations by using scalar or vector products.” …

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