We are given a rectangular prism having $x+y=0,x-y=0$ and $x=1$ as its faces. We have to find the normal vector to the plane which cuts this prism in a section that forms an equilateral triangle.
Now I couldn't visualize it properly so I used a 3-D calculator: https://www.geogebra.org/3d/trapevzc
Using this I could see that $(\sqrt2,0,1)$ is one possible normal vector but how can I prove it mathematically? Any help would be appreciated.