(i)[4]
Determine the value of $a$.
(ii)[5]
When $a$ takes this value, find the equation of the plane that contains $l$ and $m$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The two lines $l$ and $m$ are given by the equations $\mathbf{r} = a\mathbf{i} + 2\mathbf{j} + 3\mathbf{k} + \lambda(\mathbf{i} - 2\mathbf{j} + 3\mathbf{k})$ and $\mathbf{r} = 2\mathbf{i} + \mathbf{j} + 2\mathbf{k} + \mu(2\mathbf{i} - \mathbf{j} + \mathbf{k})$ respectively, with $a$ as a constant. The lines are known to intersect.