Unit 13.2 Worked Example 1

The equation of line \({{l}_{1}}\) is given by \(\mathbf{r}=\left( \begin{matrix} -12  \\-22  \\11  \end{matrix} \right)+\lambda \left( \begin{matrix}  4  \\ 4  \\  -7  \end{matrix} \right);\lambda \in \mathbb{R}\) and the point \(A\) has coordinates \(\left( 3,1,-2 \right)\).

1. Exact shortest distance of \(A\) to \({{l}_{1}}\),
2. Foot of perpendicular of \(A\) to \({{l}_{1}}\),
3. Mirror image of point \(A\) in the line \({{l}_{1}}\).