2014 SAJC P1 Q1

The line \({{l}_{1}}\) has Cartesian equation \(2x=\frac{y+2}{-7},z=1\).

Another line \({{l}_{2}}\) with vector equation \(\mathbf{r}=\left(\begin{matrix}-1\\6\\-1\end{matrix}\right)+\mu \left(\begin{matrix}0\\a\\1\end{matrix}\right)\) , where \(\mu\in\mathbb{R}\), intersects the line \({{l}_{1}}\).

Find the value of \(a\) and calculate the acute angle between the lines \({{l}_{1}}\) and \({{l}_{2}}\).[4]