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Scalar Triple Product Derivative

  1. Feb 17, 2014 #1
    1. The problem statement, all variables and given/known data

    Find an expression equivalent for the derivative of the scalar triple product

    a(t) . (b(t) x c(t))

    3. The attempt at a solution

    Initially I figured since whatever comes out of B X C is being dotted with A, I can use the derivative rules of a dot product:

    (a(t)' . (b(t) x c(t))) + ( a(t) . (b(t) x c(t))' )

    However, the solution just gives an expression for the scalar triple product in a 3x3 matrix form, that is,

    a(t) . (b(t) x c(t)) = [ a1 a2 a3
    b1 b2 b3
    c1 c2 c3 ]

    What gives?
  2. jcsd
  3. Feb 17, 2014 #2


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    Gold Member

    That would be helpful if you know how to differentiate a determinant whose entries are functions. But I like your original idea. What is the formula for ##(\vec b(t) \times \vec c(t))'##? Is there a similar formula as you used for the dot product? Just keep going...
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