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Math Help - Distance between two vector proof

  1. #1
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    Distance between two vector proof

    Define the distance between two vector u and v as
    d(u,v) = ||u-v||. Show that d(u,w) <= d(u,v) + d(v,w)

    Thanks for your help,
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  2. #2
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    Quote Originally Posted by TeeWorlves1234124 View Post
    Define the distance between two vector u and v as
    d(u,v) = ||u-v||. Show that d(u,w) <= d(u,v) + d(v,w)

    Thanks for your help,
    Are you allowed to use the fact that [tex]||a+ b||\le ||a||+ ||b||[tex]? If so this is very easy. If not, I recommend that you prove that statement first so you can use it!

    Let a= u- w and let b= w- v.
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  3. #3
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    If you meant the triangle inequalities then yes, I don't have to prove it again. I still don't get how you could prove it though.
    Thanks for replying
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  4. #4
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    NVM I got it
    Thx a bunch
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