Hi, I am having trouble with this proof, I am wondering what to do because I keep getting the wrong answer.

I want to prove

||x-y|| = ||x|| ||y|| ||x bar - y bar||

where

x and y are vectors in Rn

and u bar is defined by u/(||u||^2)

The way i started it was expanding the right side completely by using the norm formula and then simplify it into making it equal to the left, but I end up with the wrong answer and a really messy calculation. I was wondering if there was a simpler way to do this.