(a)[6]
If the acute angle between the directions of these lines is $\frac{1}{4}\pi$, determine the possible values of $a$.
(b)[5]
If, instead, the lines meet, determine the value of $a$ and the position vector of the intersection point.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The equations for two straight lines are $\mathbf{r} = \mathbf{i} + \mathbf{j} + 2a\mathbf{k} + \lambda(3\mathbf{i} + 4\mathbf{j} + a\mathbf{k})$ and $\mathbf{r} = -3\mathbf{i} - \mathbf{j} + 4\mathbf{k} + \mu(-\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$, with $a$ as a constant.