Mathematics 9709 · AS & A Level · Vectors

Vectors — practice question

Line $l$ is described by $\mathbf{r} = 4\mathbf{i} + 3\mathbf{j} - \mathbf{k} + \mu(\mathbf{i} + 2\mathbf{j} - 2\mathbf{k})$. Plane $p$ is given by $2x - 3y - z = 4$.
(i)[3]

Find the position vector of the point where $l$ and $p$ meet.

(ii)[3]

Find the acute angle formed by $l$ and $p$.

(iii)[5]

A second plane $q$ is parallel to $l$, perpendicular to $p$ and passes through the point with position vector $4\mathbf{j} - \mathbf{k}$. Find the equation of $q$, giving your answer in the form $ax + by + cz = d$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write a general point of $l$ in component form” …

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