Question 1304a

Vectors II: Lines and Planes
Equation of a Plane from the Normal Vector

Question

The line l{l} and plane p{p} are given by
l:r=(332)+λ(551),  λR,p:r(502)=43.\begin{align*} &l: \mathbf{r} = \begin{pmatrix} - 3 \\ - 3 \\ 2 \end{pmatrix} + \lambda \begin{pmatrix} 5 \\ - 5 \\ 1 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} 5 \\ 0 \\ 2 \end{pmatrix} = 43. \end{align*}
Find the acute angle, θ,{\theta,} between the the line and the plane.

Attempt

θ={\theta = }
{^\circ}

Answer

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