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Math Help - A proof of cross product and det

  1. #1
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    A proof of cross product and det

    Prove that  |a \  \times \  b   |^2 = det \left(\begin{array}{cc}(a \cdot a)&(a \cdot b)\\(a \cdot b)&(b \cdot b)\end{array}\right)

    So far I have det \left(\begin{array}{cc}(a \cdot a)&(a \cdot b)\\(a \cdot b)&(b \cdot b)\end{array}\right) = (a \cdot a) \cdot (b \cdot b) - (a \cdot b) \cdot (a \cdot b)

    But I don't know how the cross product would look like after calculation. Hints?
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  2. #2
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    I think I got it.

    I just used the properties of dot product and cross product.

    Please disregard this thread, thank you!
    Last edited by tttcomrader; January 30th 2008 at 07:26 AM.
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