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Math Help - show inequality of distance between vectors

  1. #1
    Member Jskid's Avatar
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    show inequality of distance between vectors

    Define the distance between two vectors u and v in R^n as d(u, v) = ||u-v||Show that d(u, w) <= d(u, v) + d(v, w)

    My work:
    ||u-v|| + ||v+w||=\sqrt{(u_1-v_1)^2+(u_2-v_2)^2+...+(u_n-v_n)^2}+\sqrt{(v_1-w_1)^2+(v_2-w_2)^2+...+(u_n-w_n)^2}
    Last edited by Jskid; February 12th 2011 at 07:08 PM. Reason: math tag
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  2. #2
    MHF Contributor

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    Can you use the fact that ||u+ v||\le ||u||+ ||v||?
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