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Finding orthogonal of two vectors

  1. Apr 21, 2013 #1
    1. The problem statement, all variables and given/known data

    A vector in lR 3 (basis) has vector space V with the standard inner product.

    I need to find a vector in V which is perpendicular to both vectors
    v_1 = (1,2,1)^T and v_1 = (2,1,0)^T

    2. Relevant equations

    There is no real important equations other than just using matrix and linear transformation principles.

    3. The attempt at a solution

    My attempt has gone nowhere. I used dot product to show the two vectors are not perpendicular and that's about it. It's probably real simple but I just don't get it.
  2. jcsd
  3. Apr 21, 2013 #2


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    Do you know about the cross product of vectors? If you don't, can you write down the conditions that an arbitrary vector ##\mathbf{w} = (w_1,w_2,w_3)## must satisfy to be orthogonal to those vectors?
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