# Related to orthogonality

1. Apr 19, 2005

### EvLer

In one of my hw problems we are asked to prove this:

|X + Y|^2 + |X - Y|^2 = 2|X|^2 + 2|Y|^2

It seems quite simple: I just expanded both of them (cancelled 2(X dot Y) terms) and came up with the expression on the right. Is there something I am missing or is it really that simple?

Thanks !

2. Apr 19, 2005

### Hurkyl

Staff Emeritus
It really is!

3. Apr 19, 2005

### mathwonk

linear algebra makes many questions in geometry rather trivial. for this reason high schools should teach the subject, instead of calculus, where they usually do an extremely bad job.