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Vectors Question (Orthogonality)

  1. Dec 1, 2008 #1
    1. The problem statement, all variables and given/known data

    Let u1 = [2 -2 2 ] u2 = [-2 2 1], u3 = [0 1 2]


    Use the Gram-Schmidt process to u1, u2, u3, in this order. The resulting vectors are:

    v1 = [___ ___ ___], v2 = [___ ___ ___], v3 = [___ ___ ___]

    And ß = {v1, v2, v3} is an orthongal basis for R3.

    2. Relevant equations

    v1 = u1

    v2 = u2 - u2 . v1 v1
    ------------ v1 . v1
    v3= u3 - u3 . v1 v1 - u3 . v2 v2
    ---------------v1 . v1 v2 . v2

    3. The attempt at a solution

    Well, the first one is easy.

    v1 = [2 -2 2]

    I solved v2 and got [-1, 1, 2] which was also right.

    I tried v3 based on the equation and got [1, 2/3, 4/3] which was apparently incorrect.
     
  2. jcsd
  3. Dec 1, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Why do you say "apparently" incorrect? You should have checked yourself that <2, -2, 2].[1, 2/3, 4/3]= 2- 4/3+ 8/3= 2+ 4/3 and [-1, 1, 2].[1, 2/3, 4/3]= -1+ 2/3+ 8/3= -1+ 10/3, neither of which is 0.

    If you show what you did, that is show use exactly how you used that formula, we might be able to point out an error.
     
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