Space/Plane equation/Example for intersection/2/Exercise

We consider the two sets

${}E={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid -3x+2y-6z=0\right\}}\,$

and

${}F={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid 7x-5y-4z=0\right\}}\,.$

Find a description of the intersection

${}G:=E\cap F={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid -3x+2y-6z=0{\text{ and }}7x-5y-4z=0\right\}}\,,$

similar to example.

Create a solution