Unit 13.2 Worked Example 1
The equation of line [latex]{{l}_{1}}[/latex] is given by [latex]\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}[/latex] and the point [latex]A[/latex] has coordinates [latex]\left( 3,1,-2 \right)[/latex].
(i)
Exact shortest distance of [latex]A[/latex] to [latex]{{l}_{1}}[/latex],
(ii)
Foot of perpendicular of [latex]A[/latex] to [latex]{{l}_{1}}[/latex],
(iii)
Mirror image of point [latex]A[/latex] in the line [latex]{{l}_{1}}[/latex].
