Unit 13.2 Worked Example 1

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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 \(\left( 3,1,-2 \right)\).

(i)

Exact shortest distance of \(A\) to \({{l}_{1}}\),

(ii)

Foot of perpendicular of \(A\) to \({{l}_{1}}\),

(iii)

Mirror image of point \(A\) in the line \({{l}_{1}}\).