Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

With respect to the origin $O$, the position vectors of $A$, $B$ and $D$ are $\overrightarrow{OA} = \mathbf{i} + 2\mathbf{j} + \mathbf{k}$, $\overrightarrow{OB} = 2\mathbf{i} + 5\mathbf{j} + 3\mathbf{k}$ and $\overrightarrow{OD} = 3\mathbf{i} + 2\mathbf{k}$. A further point $C$ is arranged so that $ABCD$ forms a parallelogram.
(a)[5]

Determine the position vector of $C$ and confirm that the parallelogram is not a rhombus.

(b)[3]

Find angle $BAD$, giving your answer in degrees.

(c)[2]

Find the area of the parallelogram correct to 3 significant figures.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write down or indicate $\overrightarrow{AB}$ or $\overrightarrow{AD}$ in component form” …

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