Question 1303a

Vectors II: Lines and Planes

Equation of a Plane from the Normal Vector

Question

The plane

{p}

is given by

p: \mathbf{r} \cdot \begin{pmatrix} 1 \\ 2 \\ - 5 \end{pmatrix} = 21,

Find the equation of the line

{l}

that is perpendicular to

{p}

and contains the point

{A \left( 5, - 2, - 5 \right).}

{l: }

{\mathbf{r}=\mathbf{a}+\lambda\mathbf{d}, \; \lambda \in \mathbb{R}.}

{\mathbf{a}=}

{\Biggl(}

{\Biggr), \quad}

{\mathbf{d}=}

{\Biggl(}

{\Biggr)}