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Math Help - Vector Question

  1. #1
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    Vector Question

    if F = x^3yi +(y^2x -zx)j +(z^3 x^2 +y^2)k  verify the identity

    \nabla \wedge (\nabla\wedge F) = \nabla(\nabla\cdot F) - \nabla^2 F

    my attempt

    i found \nabla\wedge(\nabla \wedge F) to be (2y+6xz^2)i -(1+3x^2)j +(-2z^3-2)k

    but when i calculated \nabla(\nabla\cdot F) i got (6x+2y+6z^2 x, 2x, 6zx^2) and

    \nabla^2 F = (6+6z^2,0,6x^2)

    can someone tell me where i went wrong, am i using the wrong fomula?
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  2. #2
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    Quote Originally Posted by iLikeMaths View Post
    if F = x^3yi +(y^2x -zx)j +(z^3 x^2 +y^2)k verify the identity

    \nabla \wedge (\nabla\wedge F) = \nabla(\nabla\cdot F) - \nabla^2 F

    my attempt

    i found \nabla\wedge(\nabla \wedge F) to be (2y+6xz^2)i -(1+3x^2)j +(-2z^3-2)k

    but when i calculated \nabla(\nabla\cdot F) i got (6x+2y+6z^2 x, 2x, 6zx^2) and

    \nabla^2 F = (6+6z^2,0,6x^2)

    can someone tell me where i went wrong, am i using the wrong fomula?
    The formula is right. Some of your terms are wrong. Here's what I got.

    \nabla\times(\nabla \times F) = (2y+6xz^2)i +3x^2 j +(-2z^3-2)k

    \nabla(\nabla\cdot F) = (6xy+2y+6xz^2)i + (2x+3x^2)j + (6 x^2z)K

    \nabla^2 F = 6xyi + 2x j +(2 + 6x^2z + 2z^3)k
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