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Math Help - Cross Product Help

  1. #1
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    Cross Product Help

    Find all the vectors u that satisfy the equation <1,1,1> X u = <0,0,1>



    I don't know if there are multiple ways of doing this, but we're using the determinant! :)
    (The answer in the back of the book is <u3-1, u3+1, u3> I just don't know how to get to it!)
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  2. #2
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    Re: Cross Product Help

    Quote Originally Posted by jessicadowning View Post
    Find all the vectors u that satisfy the equation <1,1,1> X u = <0,0,1>



    I don't know if there are multiple ways of doing this, but we're using the determinant!
    (The answer in the back of the book is <u3-1, u3+1, u3> I just don't know how to get to it!)
    Write \displaystyle \begin{align*} \mathbf{u} = <x, y, z> \end{align*}, then \displaystyle \begin{align*} <1, 1, 1> \times <x, y, z> &= \left| \begin{matrix} i & j & k \\ 1 & 1 & 1 \\ x & y & z  \end{matrix}  \right| \end{align*}. Evaluate this determinant, and then set the resulting i component to 0, the resulting j component to 0, and the resulting k component to 1 to solve for x, y, z.
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  3. #3
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    Re: Cross Product Help

    Could you possibly show me how to solve from there? This is where I originally got stuck... lol
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    Re: Cross Product Help

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