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Advanced Vecor calculus - Cross Product

  1. Jan 12, 2012 #1
    1. The problem statement, all variables and given/known data

    For arbitrary vector fields A and B show that;

    ∇ ^ (A^B) = (∇ . B)A - (∇.A)B + (B.∇)A - (A.∇)B

    2. Relevant equations

    where (A.∇)B = ((A.∇)Bx, (A.∇)By, (A.∇)Bz)

    and (A.∇)f = Ax δf/δx + Ay δf/δy + Az δf/δz = (Ax, Ay, Az)( δf/δx, δf/δy, δf/δz)f

    3. The attempt at a solution

    I asked my lecturer and he said something about finding the x-component and wrote

    δ/dy(AyBz - AzBy) - δ/δz(AxBy - AyBx)

    on my work but I don't really see how this applies...

    Any help would be really appreciated :D
     
  2. jcsd
  3. Jan 12, 2012 #2

    lanedance

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    how about wirting it out component by component? Long, but is a useful exercise

    Also I am assuming "^" means cross product?
     
  4. Jan 12, 2012 #3
    I thought that but I don't know how to write it out like that..

    Is my lecturer correct in his definiton of the x-component? and if so do you know how he got it to be that?

    and yes ^ means cross product I didn't want any confusion with multiplication.
     
  5. Jan 12, 2012 #4

    lanedance

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    Homework Helper

     
    Last edited: Jan 12, 2012
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