(a)[4]
Since $l$ and $m$ intersect, show that $2b - a = 4$.
(b)[4]
If $l$ and $m$ are also perpendicular, find the values of $a$ and $b$.
(c)[2]
When $a$ and $b$ have these values, find the position vector of the point where $l$ and $m$ intersect.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The vector equations for the lines $l$ and $m$ are $\mathbf{r} = -\mathbf{i} + 3\mathbf{j} + 4\mathbf{k} + \lambda(2\mathbf{i} - \mathbf{j} - \mathbf{k})$ and $\mathbf{r} = 5\mathbf{i} + 4\mathbf{j} + 3\mathbf{k} + \mu(a\mathbf{i} + b\mathbf{j} + \mathbf{k})$ respectively, where $a$ and $b$ are constants.