2

2. [Maximum mark: 5]

The line $L_1$ is defined by the Cartesian equation $\frac{x - 1}{2} = \frac{y + 2}{3} = z$.

(a) Find a vector equation of $L_1$. [2]

A second line $L_2$ is defined by the vector equation $\mathbf{r} = \begin{pmatrix} 0 \\ 4 \\ -8 \end{pmatrix} + t \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix}$, where $t \in \mathbb{R}$.

(b) Find the coordinates of the point where $L_1$ and $L_2$ intersect. [3]