The plane equations for $m$ and $n$ are $x + 2y - 2z = 1$ and $2x - 2y + z = 7$ respectively, and the line $l$ is given by $\mathbf{r} = \mathbf{i} + \mathbf{j} - \mathbf{k} + \lambda(2\mathbf{i} + \mathbf{j} + 2\mathbf{k})$.
(i)[3]
Demonstrate that $l$ is parallel to $m$.
(ii)[3]
Determine the position vector of the point of intersection of $l$ and $n$.
(iii)[6]
A point $P$ on $l$ has equal perpendicular distances from $m$ and $n$. Find the position vectors of the two possible locations of $P$ and calculate the distance between them.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Insert the coordinates of a general point on $l$ into the equation of plane $m$” …