Question 1304b

Vectors II: Lines and Planes

Equation of a Plane from Direction Vectors

Question

The line

{l}

and plane

{p}

are given by

\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 5 \\ - 1 \\ - 5 \end{pmatrix} + \lambda \begin{pmatrix} 4 \\ 5 \\ - 5 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = 5. \end{align*}

Find the coordinates of the point of intersection between the the line and the plane.

Your answer:

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