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Math Help - Help with algebra proof

  1. #1
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    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!
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  2. #2
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    Re: Help with algebra proof

    1) What's "theta"?
    2) What if v = 0? Are you SURE you have the problem stated correctly?
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  3. #3
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    Re: Help with algebra proof

    Quote Originally Posted by Mitsuruangel View Post
    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...
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