The equations of the lines $l$ and $m$ are $\mathbf{r} = 3\mathbf{i} - 2\mathbf{j} + \mathbf{k} + \lambda(-\mathbf{i} + 2\mathbf{j} + \mathbf{k})$ and $\mathbf{r} = 4\mathbf{i} + 4\mathbf{j} + 2\mathbf{k} + \mu(a\mathbf{i} + b\mathbf{j} - \mathbf{k})$, respectively, with $a$ and $b$ as constants.
(i)[4]
Since $l$ and $m$ intersect, show that $2a - b = 4$.
(ii)[4]
Also given that $l$ and $m$ are perpendicular, find the values of $a$ and $b$.
(iii)[2]
With these values of $a$ and $b$, find the position vector of the point of intersection of $l$ and $m$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write a general point on $l$ or $m$ in component form.” …