(i)[5]
Determine the length of the perpendicular from $P$ to $l$, and give your answer to 3 significant figures.
(ii)[5]
Find the equation of the plane that contains $l$ and $P$, and present it in the form $ax + by + cz = d$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
Point $P$ is given by the position vector $3\mathbf{i} - 2\mathbf{j} + \mathbf{k}$. Line $l$ is defined by $\mathbf{r} = 4\mathbf{i} + 2\mathbf{j} + 5\mathbf{k} + u(\mathbf{i} + 2\mathbf{j} + 3\mathbf{k})$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find $\vec{PQ}$ or $\vec{QP}$ for a general point $Q$ on $l$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI