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Math Help - Vector Span and Orthogonality

  1. #1
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    Vector Span and Orthogonality

    Prove thath if v, w, and x are in R2 or R3 an v is orthogonal to both w and x, then v is orthogonal to every vector span in {w, x}.

    I'm totally lost on this problem. So far what I've got is that
    v . w = 0
    v . x = 0

    v1w1 + .... + vnwn = 0
    v1x1 + .... + vnxn = 0
    v1x1 + .... + v1x1 = v1w1 + .... + vnwn
    v1(x1 - w1) + .... + vn (xn - wn) = 0
    (I'm not even sure if this part is useful or not)

    Let's say there is a y that is a vector in the span of {w, x}. How would I prove that v . y = 0?

    Thanks
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  2. #2
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    Quote Originally Posted by Brokescholar View Post
    Prove thath if v, w, and x are in R2 or R3 an v is orthogonal to both w and x, then v is orthogonal to every vector span in {w, x}.
    Any vector in the spam of \{ \bold{w},\bold{x} \} can be written in the form a\bold{w}+b\bold{x}.

    Then \bold{v}\cdot (a\bold{w}+b\bold{x}) = a \bold{v}\cdot \bold{w} + b \bold{v}\cdot \bold{x} = a\bold{0}+b\bold{0} = \bold{0}.
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