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Proving a given vector equation

  1. Dec 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove ||u+v||^2 + ||u-v||^2=2||u||^2+2||v||^2

    2. Relevant equations
    * This is the part I can't figure out*

    3. The attempt at a solution
    anybody got an idea where I can start? I can't seem to remember the property I can use to simplify ||u+v||^2

    P.S sorry for the vague title, i really didn't know what to put in there.
     
    Last edited: Dec 10, 2014
  2. jcsd
  3. Dec 10, 2014 #2

    jedishrfu

    Staff: Mentor

    Are u and v vectors?
     
  4. Dec 10, 2014 #3
    Yes! sorry I should have italized them , copy pasted it, Ill edit it right now
     
  5. Dec 10, 2014 #4

    jedishrfu

    Staff: Mentor

    What can you say about u+v and u-v?
     
  6. Dec 10, 2014 #5
    Hmmmm, Not too sure what I can say, but geometrically they are two sides of a parallelogram, and u+v / u-v is the line across it
     
  7. Dec 10, 2014 #6

    jedishrfu

    Staff: Mentor

    Have you tried using the vector dot product for u+v and for u-v?

    Hint replace the (u+v)^2 with its dot product
     
    Last edited: Dec 10, 2014
  8. Dec 10, 2014 #7
    Ahhh I see so I do u+v dot u+v ? then just distribute and use the idea that u dot u = ||u||?
     
  9. Dec 10, 2014 #8

    jedishrfu

    Staff: Mentor

    I think you have it now. I hope my hint wasn't too obvious.
     
  10. Dec 10, 2014 #9
    nope lead me in the right direction. Thank you so much!
     
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