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Math Help - Curl (F x G) proof

  1. #1
    Senior Member
    Joined
    Oct 2008
    Posts
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    Curl (F x G) proof

    Hi

    Im a bit stuck

    I have done the cross multiplication

    i --- j --- k
    F1 --- F2 --- F2
    G1 ---G2 --- G3

    (F2G3 - F3G2)i + (G1F3 - G3F1)j + (F1G2 - F2G1)k

    Then cross multilpies it again

    so

    i --------------------- j -------------------- k

    d/dx -------------------- d/dy ---------------------- d/dz

    F2G3 - F3G2-------------- G1F3 - G3F1--------------------- F1G2 - F2G1

    And done this and got

    (d/dy(F1G2 - F2G1) - d/dz (G1F3 - G3F1))i + (d/dz(F2G3 - F3G2) - d/dx(F1G2 - F2G1))j + (d/dx(G1F3 - G3F1) - d/dy(F2G3 - F3G2))k

    Now i dont know how to shows this is FdivG - GdivF + (G.Delta)F - (F.Delta)G

    Thanks
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  2. #2
    MHF Contributor

    Joined
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    First, go ahead and finish the derivative: (F12G2+ F1G22- F22G1- F2G12- G12F3- G1F33+ G33F1+ G3F13)i etc. Tedious and complicated but doable. Then do the same thing for F div G- G div F+ (G.Delta)F- (F.Delta)G and compare.
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