Question 1304e

Vectors II: Lines and Planes
Cartesian and Vector Equation of a Plane

Question

The line l{l} and the plane p{p} are given by
l:r=(11−4)+λ(522),  λ∈R,p:r⋅(2−4−1)=5.\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 1 \\ 1 \\ - 4 \end{pmatrix} + \lambda \begin{pmatrix} 5 \\ 2 \\ 2 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} 2 \\ - 4 \\ - 1 \end{pmatrix} = 5. \end{align*}
What is the relationship between the line and the plane?

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