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Adding vectors in R^n

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Let x and y be vectos in R^n such that ||x|| = ||y|| = 1 and x^T * y = 0. Use Eq. (1) to show that ||x-y|| = sqrt(2).

    2. Relevant equations

    Eq. (1): ||x|| = sqrt(x^T * X)

    3. The attempt at a solution

    I could figure this out knowing that the dot product of the vectors is zero so the are perpendicular, the two sides of the triangle are 1 so the distance is sqrt(2) but this problem wants the answer to be found with Eq. (1) and I don't know how to do that and how to find ||x-y||.

    Thanks for the help
     
  2. jcsd
  3. Oct 12, 2009 #2

    HallsofIvy

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    Your formula says that ||x- y||= [itex]\sqrt{(x- y)^T(x- y)}= \sqrt{x^Tx- x^Ty- y^Tx+ y^Ty}[/itex]. Both [itex]x^Ty[/itex] and [itex]y^Tx[/itex] are 0.
     
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