Question 1303e

Vectors II: Lines and Planes

Cartesian and Vector Equation of a Plane

Question

Plane

{p}

is given by the equation

p: \mathbf{r} = \begin{pmatrix} 3 \\ - 1 \\ - 4 \end{pmatrix} + \lambda \begin{pmatrix} - 1 \\ 5 \\ 3 \end{pmatrix} + \mu \begin{pmatrix} - 4 \\ - 1 \\ 5 \end{pmatrix}, \; \lambda,\mu \in \mathbb{R}.

Express the equation of the plane

{p}

in scalar product form

{\mathbf{r}\cdot \mathbf{n} = k.}

{p: }

{\mathbf{r}\cdot}

{\Biggl(}

{\Biggr)}

{=}