# Thread: Help with algebra proof

1. ## Help with algebra proof

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!

2. ## Re: Help with algebra proof

1) What's "theta"?
2) What if v = 0? Are you SURE you have the problem stated correctly?

3. ## Re: Help with algebra proof

Originally Posted by Mitsuruangel
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!
I suggest you read this... You are trying to prove the Reverse Triangle Inequality...