Question 1302d

Vectors II: Lines and Planes

Perpendicular Distance between Lines

Question

The line

{l}

is given by

l_1: \mathbf{r} = \begin{pmatrix} - 5 \\ - 1 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 4 \\ - 3 \end{pmatrix}, \; \lambda \in \mathbb{R}.

Find the perpendicular distance between the line and the point

{B \left( - 4, - 2, 5 \right).}