Question

prove that if vectors V and U are perpendicular to, then
|| u ||^2 + || v ||^2 = || u-v ||^2

I understand that it involves the property that dot product of 2 perpendicular vectors is 0 but I don't know how to start

Answer 1

Write <x,y> for the inner product of two vectors x and y.

Then remember that
|| u ||^2 = <u,u>.

To prove your identity, consider
<u-v,u-v>

Answer 2

Show that
<u-v,u-v>
equals both sides of the identity.

In other words, evaluate <u-v,u-v> two ways.

Answer 3

thanks!