If I have z= ||v||u + ||u||v, can I say that (z/uv) = (||v||/v) + (||u||/u) ?

Assuming that those bold letters are vectors, division as you have used it there really isn't defined.

 

i.e. if u = [1 0 13]

and if v = [-4 7 2] what is u/v or v/u ?

 

See: http://mathworld.wolfram.com/VectorDivision.html

Bignose is quite correct; vector division isn't defined in any form so you can't use your stated "identity".

Yeah, I see what I did wrong. I should have divided by the norms instead. Thanks for the replies