Unit 13.2 Worked Example 2
The line ${{l}_{2}}$ passes through $A\left( 3,1,-2 \right)$ and is parallel to the direction vector $\left( \begin{matrix}7 \\15 \\1 \\\end{matrix} \right)$.
${{l}_{2}}$ intersects ${{l}_{1}}:\mathbf{r}=\left( \begin{matrix} -12 \\ -22 \\ 11 \\\end{matrix} \right)+\lambda \left( \begin{matrix}4 \\ 4 \\ -7 \\\end{matrix} \right);\lambda \in \mathbb{R}$ at $C$.
Find
(i)
the coordinates of $C$,
(ii)
the acute angle between ${{l}_{1}}$ and ${{l}_{2}}$,
(iii)
the vector line equation of mirror image of ${{l}_{2}}$ in ${{l}_{1}}$.
