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Vector proofs

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Proof that the following statements are all equivalent. First assume that none of the vectors are zero vectors. Then prove it in the degenerate case, where the vectors are zero vectors.

    1) [itex] u = kv [/itex] where k is a scalar.
    2) [itex] u \times v = 0 [/itex]
    3) [itex] u \cdot v = ||u|| ||v|| [/itex]
    4) [itex] ||u+v|| = ||u|| + ||v|| [/itex]

    2. Relevant equations



    3. The attempt at a solution
    In order to prove this, we must show that the truth of each of these statements implies the truth of the other. I was able to show that the truth of the first statement implies the truth of the other three, but have not been able to show the converses. For example, how would I prove that (4) implies (1)? I would need to come up with some scalar k such that u = kv? But how could I generate this scalar?

    Any ideas are appreciated.

    BiP
     
  2. jcsd
  3. Oct 18, 2012 #2

    LCKurtz

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    You don't have to show they all imply 1 directly. What about 4 implies 3 implies 1? Start by squaring 4.
     
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