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Math Help - find a vector that has this characteristic

  1. #1
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    find a vector that has this characteristic

    find a vector u=(a,b,c) where a,b,c are not all 0 so that u is orthogonal to both x=(1,2,1) and y=(1,-1,1)

    Can I use the cross product on x and y or would that be incorrect?
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  2. #2
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    Quote Originally Posted by superdude View Post
    find a vector u=(a,b,c) where a,b,c are not all 0 so that u is orthogonal to both x=(1,2,1) and y=(1,-1,1)

    Can I use the cross product on x and y or would that be incorrect?

    Of course you can cross multiply the vectors and that's correct: the cross product is a vector orthogonal to both original ones.

    Tonio
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  3. #3
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    There is another method except cross product.

    <br />
A=\begin{bmatrix} \vec{x} &\vec{y}<br />
 \end{bmatrix}~,<br />
 ~\vec{u}\in im(A)^{\perp}=\ker(A^{T})<br />
 =\ker\begin{bmatrix}<br />
 1 &2 &1 \\<br />
 1 &-1 &1 \\<br />
 \end{bmatrix} \\<br />

    <br />
 =\ker\begin{bmatrix}<br />
 1 &2 &1 \\<br />
 0 &-3 &0 \\<br />
 \end{bmatrix}<br />
 =\ker\begin{bmatrix}<br />
 1 &0 &1 \\<br />
 0 &1 &0 \\<br />
 \end{bmatrix}<br />
 =span( \begin{bmatrix}<br />
 -1 \\0 \\1<br />
 \end{bmatrix} ) \\<br />

    <br />
 \rightarrow b=0,|a|=|c|\neq 0,a=-c<br /> <br />

    If dimension is high, cross product is complex
    Last edited by math2009; February 9th 2010 at 02:17 PM.
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