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Homework Help: Determinates to Calculate Cross Product

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Not really a homework problem, just a general question.

    2. Relevant equations
    Sorry, I don't yet know how to create arrays/matrices in latex (this is a gif)

    3. The attempt at a solution
    In the above image, why is [itex]c_{1}[/itex] positive, [itex]c_{2}[/itex] negative, and [itex]c_{3}[/itex] positive?

    Aside from that, I think I understand the rest. I would assume c from the formula to be the unit vectors denoting direction, A would be the first vector in the product, and B would be the second. From there,

    [itex]c_{1}[/itex] times [itex](a_{2}b_{3} - b_{2}a_{3})[/itex]

    would be the [itex]c_{1}[/itex] component of the product and so on...

    But why would the y/j component be negative in the formula?
  2. jcsd
  3. Sep 18, 2011 #2


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  4. Sep 18, 2011 #3
    Ahh, I see. So it's going to alternate every time as the exponent (i+j) becomes odd/even. I can see how this would get really tedious for matrices larger than 3x3.

    Thanks for the information!
  5. Sep 18, 2011 #4
    It's just the nature of it isn't it? It's like looking at the mirror
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