Question 1304c

Vectors II: Lines and Planes

Equation of a Plane from III

Question

The line

{l}

and plane

{p}

are given by

\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 2 \\ - 2 \\ 5 \end{pmatrix} + \lambda \begin{pmatrix} 4 \\ 0 \\ - 5 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} 5 \\ 2 \\ 4 \end{pmatrix} = - 41. \end{align*}

Find the perpendicular distance between

{l}

and

{p.}