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Test Question: Vector Proof Help

  1. Feb 27, 2008 #1
    Sorry for notation guys, but I don't know how to use LaTex.

    1. The problem statement, all variables and given/known data
    True or false, there exists a vector v (or set of vectors) in R3 such that v*v = ||v|| (v dot v equals the magnitude of v).


    2. Relevant equations
    At first I thought this was false, but then I considered an arbitrary unit vector v=(1/(14)/\(-1/2)*(1,2,3)...in words: one over the square root of fourteen times the vector one, two, three (the unit vector of (1,2,3)).


    3. The attempt at a solution

    Taking v*v, u get (1*1)/14 + (2*2)/14 + (3*3)/14 = 1/14 + 4/14 + 9/14 = 14/14 = 1, which is trivial for a unit vector. Also, the magnitude is just the square root of this answer, since the components are already squared for dotting itself, which is one; again, trivial. Am I correct or can I not consider a unit vector?
     
  2. jcsd
  3. Feb 27, 2008 #2
    You just demonstrated that the answer it true. Why are you doubting yourself?
     
  4. Feb 27, 2008 #3
    I am doubting myself because I had strong opposition from 3 classmates that for some reason you can't use a unit vector for the proof.
     
  5. Feb 27, 2008 #4
    Well, we can't really tell you if it said that you can't use unit vectors. Regardless, it's clearly true for any unit vector because, using your notation, the equation says ||v||^2 = v*v = ||v||.

    Edit: Yeah, I'm really out of it today.
     
    Last edited: Feb 27, 2008
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