The planes $m$ and $n$ are given by the equations $3x + y - 2z = 10$ and $x - 2y + 2z = 5$, respectively. The line $l$ is given by $\mathbf{r} = 4\mathbf{i} + 2\mathbf{j} + \mathbf{k} + \lambda(\mathbf{i} + \mathbf{j} + 2\mathbf{k})$.
(i)[3]
Show that $l$ is parallel to $m$ by using the given equations.
(ii)[3]
Calculate the acute angle between the planes $m$ and $n$.
(iii)[4]
A point $P$ is on line $l$. Its perpendicular distance from plane $n$ is $2$. Find the position vectors of the two possible positions of $P$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Expand the scalar product of a normal to plane $m$ and a direction vector of line $l$” …