The two lines are given by $\mathbf{r} = \mathbf{i} + 2\mathbf{j} + \mathbf{k} + \lambda(a\mathbf{i} + 2\mathbf{j} - \mathbf{k})$ and $\mathbf{r} = 2\mathbf{i} + \mathbf{j} - \mathbf{k} + \mu(2\mathbf{i} - \mathbf{j} + \mathbf{k})$, where $a$ is a constant.
(a)[5]
If the two lines intersect, determine the value of $a$ and the position vector of their point of intersection.
(b)[6]
If the acute angle between the directions of the two lines is $\cos^{-1}\left(\frac{1}{6}\right)$, determine the two possible values of $a$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write the general point in the correct component form” …