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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:

Question and Diagram

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!

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    It seems that if you did read the FAQ for homework questions, you misunderstood it. It says: "Show your work. You should definitely include any partial work you have done." How is someone going to improve on your proof of (i) if you don't tell us what it is?2011-10-21

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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.