This is a problem that I was set by my physics teacher but really seems to be more of a maths problem than a physics one.
I have read the guidelines for homework questions and I think I've met all the criteria, I have tried very hard to solve this but I've had no luck, though I did manage to prove the first one, but in a very inelegant manner that I was hoping someone could improve on. Anyway here's the question:
I think however the question is wrong. The prism is not a square prism. It could just be me though.
Thanks for your help in advance!
Here are some hints:
Use the information given to get a precise quantitative picture of the quadrilateral $ABCD$. How exactly is the point $E$ situated therein?
Introduce a $(x,y,z)$-coordinate system with origin at $E$, $A$ and $C$ on the $x$-axis, $B$ and $D$ on the $y$ axis. Now use the formulae of three-dimensional analytic geometry.