Space/Planed/Point on two planes/1/Exercise

We consider the three planes ${}E,F,G$ in ${}\mathbb {Q} ^{3}$, given by the following equations.

1. ${}E={\left\{(x,y,z)\in \mathbb {Q} ^{3}\mid 5x-4y+3z=2\right\}}\,,$

2. ${}F={\left\{(x,y,z)\in \mathbb {Q} ^{3}\mid 7x-5y+6z=3\right\}}\,,$

3. ${}G={\left\{(x,y,z)\in \mathbb {Q} ^{3}\mid 2x-y+4z=5\right\}}\,.$

Determine all points in ${}E\cap F\setminus E\cap F\cap G$.

Create a solution