(a)[2]
State a vector equation for the line $l$.
(b)[3]
The position vector of point $B$ from the origin $O$ is $\overrightarrow{OB} = -ti + 4j + 3k$, where $t$ is a constant. The line $l$ also goes through $B$. Determine the value of $t$.
(c)[5]
The line $m$ is given by the vector equation $\mathbf{r} = 5\mathbf{i} - \mathbf{j} + 2\mathbf{k} + \mu(a\mathbf{i} - \mathbf{j} + 3\mathbf{k})$. The acute angle between the directions of $l$ and $m$ is $\theta$, with $\cos\theta = \frac{1}{\sqrt{6}}$. Find the possible values of $a$.