Ok, I'm not very good at algebra proofs and there is one on my assignment that I am stuck on. It seems easy but I just can't figure it out.

If 0<theta<(pi/2) and u and v are vectors in R3

Prove that

||u-v||<||u||+||v||

This is as far as I got:

=sqrt(u-v)(u-v)<sqrt(u)(u) + (v)(v)

=sqrt((u*u)+(2u*v)+(v*v)) < sqrt(u)(u) + (v)(v)

And I don't know whre to go from there

If someone could walk me through it I would really appreciate it!