Question 1303a

Vectors II: Lines and Planes

Equation of a Plane from the Normal Vector

Question

The line

{l}

is given by

l: \mathbf{r} = \begin{pmatrix} - 3 \\ 5 \\ 1 \end{pmatrix} + \lambda \begin{pmatrix} - 5 \\ - 4 \\ - 5 \end{pmatrix},

Find the equation of the plane

{p}

that is perpendicular to

{l}

and contains the point

{B \left( 5, 1, 4 \right).}

{p: }

{\mathbf{r}\cdot}

{\Biggl(}

{\Biggr)}

{=}