(a)[4]
Show that $OABC$ forms a rectangle.
(b)[4]
Use a scalar product to determine the acute angle between the diagonals of $OABC$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Taking the origin $O$ as the reference point, the position vectors of $A$, $B$ and $C$ are $\overrightarrow{OA} = 5\mathbf{i} - 2\mathbf{j} + \mathbf{k}$, $\overrightarrow{OB} = 8\mathbf{i} + 2\mathbf{j} - 6\mathbf{k}$ and $\overrightarrow{OC} = 3\mathbf{i} + 4\mathbf{j} - 7\mathbf{k}$.
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