(i)[3]
Find the values of $q$ such that $\mathbf{u}$ is perpendicular to $\mathbf{v}$.
(ii)[4]
Find the angle between $\mathbf{u}$ and $\mathbf{v}$ for $q = 0$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The vectors $\mathbf{u}$ and $\mathbf{v}$ are given by $\mathbf{u} = \begin{pmatrix} q \\ 2 \\ 6 \end{pmatrix}$ and $\mathbf{v} = \begin{pmatrix} 8 \\ q-1 \\ q^2-7 \end{pmatrix}$, with $q$ as a constant.
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This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Form scalar product $\mathbf{u}\cdot\mathbf{v}=8q+2q-2+6q^2-42” …
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