Vectors - Distance from a Point to a Line

Vectors - Distance from a Point to a Line

TGM Original Questions

The line \({{l}_{3}}\) passes through \(B\left( 7,4,-5 \right)\) and is parallel to \({{l}_{1}}:\mathbf{r}=\left( \begin{matrix} -12  \\-22  \\ 11  \end{matrix} \right)+\lambda \left( \begin{matrix} 4  \\  4  \\   -7  \end{matrix} \right);\lambda \in \mathbb{R}\).

Find the perpendicular distance between \({{l}_{1}}\) and \({{l}_{3}}\).

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Answer:\(15.5\) units

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