Vectors - Perpendicular Projection and Reflection in a Line

Vectors - Perpendicular Projection and Reflection in a Line

The line equation \({l}:\mathbf{r}=\left( \begin{matrix}-2\\1\\3\end{matrix}\right)+\lambda \left( \begin{matrix}1\\-2\\1\end{matrix} \right)\). Find the position vector of the foot \(N\) of the perpendicular from \(A\left( \begin{matrix}0\\2\\-3\end{matrix} \right)\) . Hence find the position vector of the image of \(A\) in the line \(l\) .

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Answer:\(\overrightarrow{ON}=\begin{pmatrix}-3 \\ 3 \\ 2\end{pmatrix}\), and \(\overrightarrow{OA'}=\begin{pmatrix}-6 \\ 4 \\ 7\end{pmatrix}\).

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