How could you use the properties of the dot product to prove the following identities: (where u and v denote vectors in Rn)
a) ||u + v||^2 + ||u-v||^2 = 2(||u||^2 + ||v||^2)
b) ||u + v||^2 - ||u-v||^2 = 4u dot v
Note:
dot = dot product
^ = power
||= distance