Question 1304a

Vectors II: Lines and Planes

Equation of a Plane from the Normal Vector

Question

The line

{l}

and plane

{p}

are given by

\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 1 \\ - 1 \\ - 1 \end{pmatrix} + \lambda \begin{pmatrix} - 4 \\ 5 \\ 5 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} 1 \\ 4 \\ - 1 \end{pmatrix} = 31. \end{align*}

Find the acute angle,

{\theta,}

between the the line and the plane.

{\theta = }

{^\circ}