(i)[5]
Find the position vector of $D$, and show that the parallelogram is a rhombus.
(ii)[5]
Plane $p$ is parallel to $OA$, and the line $BC$ lies in $p$. Find the equation of $p$, with your answer written in the form $ax + by + cz = d$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Points $A$, $B$ and $C$ have position vectors relative to the origin $O$, namely $\overrightarrow{OA} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$, $\overrightarrow{OB} = 4\mathbf{j} + \mathbf{k}$ and $\overrightarrow{OC} = 2\mathbf{i} + 5\mathbf{j} - \mathbf{k}$. A further point $D$ is chosen so that quadrilateral $ABCD$ is a parallelogram.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Give, or make clear, $\overrightarrow{AB}$ or $\overrightarrow{BC}$ in component form, or the position vector of the midpoint of $AC$.” …
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