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||v - u|| >= | ||v||-||u|| |

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data
    Prove : ||V - U|| => | ||V||-||U|| |
    V and U are vectors

    2. Relevant equations
    Maybe the dot product formula: ||A||*||B||cosθ


    3. The attempt at a solution
    ==> ||V - U||2 >= (||V||-||U||)2
    ==> (V-U) . (V-U) >= ||V||2 +||U||2 - 2||U||*||V||
    ==> V.V + U.U -2U.V >= V.V + U.U - 2||U||*||V||
    ==> -2U . V >= -2 ||U||*||V||

    I don't know how to go on from here. I always get a nonsensical answer if I try to simplify this. Am I using the right approach?
     
    Last edited: Sep 25, 2011
  2. jcsd
  3. Sep 25, 2011 #2

    LCKurtz

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    You have the inequality backwards above.

    Hint: ||u|| = ||(u - v) + v|| ≤ ...
     
  4. Sep 25, 2011 #3
    Can you give me another hint please?
     
  5. Sep 25, 2011 #4

    LCKurtz

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    What did you try with my hint? What might go after the ≤ ?
     
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