Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

Taking the origin $O$ as the reference point, the position vectors of points $A$, $B$ and $C$ are $\overrightarrow{OA}=4\mathbf{i}-2\mathbf{j}$, $\overrightarrow{OB}=2\mathbf{i}+8\mathbf{j}+4\mathbf{k}$, and $\overrightarrow{OC}=-2\mathbf{i}+6\mathbf{k}$. Point $M$ is the midpoint of $AB$, as the diagram shows.
(a)[2]

Find the required vectors $\overrightarrow{MB}$ and $\overrightarrow{MC}$.

(b)[3]

Calculate the exact value of the cosine of angle $CMB$.

(c)[4]

Hence or by another route, find the exact area of triangle $ABC$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Thus, $\overrightarrow{MB}=-\mathbf{i}+5\mathbf{j}+2\mathbf{k}$” …

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