(a)[3]
Since $|\overrightarrow{AB}| = |\overrightarrow{BC}|$ is given, determine the value of $b$.
(b)[2]
$A$, $B$, $C$ and $D$ are the vertices of a rhombus. Determine the position vector of $D$.
(c)[3]
Calculate the angle $ABC$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Relative to the origin $O$, the position vectors for $A$, $B$ and $C$ are given by $\overrightarrow{OA} = 2\mathbf{i} - \mathbf{j} - 6\mathbf{k}$, $\overrightarrow{OB} = b\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}$ and $\overrightarrow{OC} = -4\mathbf{i} + 5\mathbf{j} - 2\mathbf{k}$.
Worked solution & mark scheme
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