(i)[3]
Determine the position vector of $A$.
(ii)[4]
Calculate the acute angle between $l$ and $p$.
(iii)[4]
Determine the equation of the line that lies in $p$ and intersects $l$ at right angles.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The line $l$ is represented by $\mathbf{r} = 5\mathbf{i} - 3\mathbf{j} - \mathbf{k} + \lambda(\mathbf{i} - 2\mathbf{j} + \mathbf{k})$. The plane $p$ is represented by $(\mathbf{r} - \mathbf{i} - 2\mathbf{j}) \cdot (3\mathbf{i} + \mathbf{j} + \mathbf{k}) = 0$. The line $l$ meets the plane $p$ at the point $A$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute for $\mathbf{r}$ and expand the scalar product so that an equation in $\lambda$ is obtained.” …
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