Question 1303c

Vectors II: Lines and Planes

Equation of a Plane from III

Question

The line

{l}

and the plane

{p_1}

are given by

\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 4 \\ 4 \\ 1 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ - 1 \\ 2 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p_1: \mathbf{r} \cdot \begin{pmatrix} 1 \\ - 8 \\ - 1 \end{pmatrix} = - 29. \end{align*}

Find the equation of the plane

{p}

that contains

{l_1}

and is perpendicular to

{p_1.}

{p: }

{\mathbf{r}\cdot}

{\Biggl(}

{\Biggr)}

{=}