Question 1303b

Vectors II: Lines and Planes

Equation of a Plane from Direction Vectors

Question

The lines

{l_1}

and

{l_2}

are given by

\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} 2 \\ 2 \\ - 2 \end{pmatrix} + \lambda \begin{pmatrix} - 5 \\ - 2 \\ 2 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} 2 \\ 2 \\ - 2 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}

Find the equation of the plane

{p}

containing both

{l_1}

and

{l_2.}

{p: }

{\mathbf{r}\cdot}

{\Biggl(}

{\Biggr)}

{=}