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 ${{l}_{2}}$.
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