Question 1302d

Vectors II: Lines and Planes

Perpendicular Distance between Lines

Question

The line

{l}

is given by

l_1: \mathbf{r} = \begin{pmatrix} 0 \\ - 5 \\ 1 \end{pmatrix} + \lambda \begin{pmatrix} - 1 \\ 1 \\ - 2 \end{pmatrix}, \; \lambda \in \mathbb{R}.

Find the perpendicular distance between the line and the point

{B \left( - 1, - 4, 4 \right).}