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Math Help - Differential Equation: Cross product Query

  1. #1
    Senior Member bugatti79's Avatar
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    Differential Equation: Cross product Query

    Can anyone check I have calculated correctly the cross product of 2 vectors..
    See attached.
    It is part of a problem to solve a quasi linear equation in which a horizontal plane cuts a sphere.
    I am to check that the 2 functions phi and psi are linearly independent if there cross product is not equal to 0. Although it a very simple problem, I havent come across it before.

    Thanks
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    If \nabla  (\phi)=(2x,2y,2u) and \nabla  ( \psi)=(0,0,1) then, \nabla  (\phi)\times \nabla  ( \psi)=(2y,-2x,0) and this means that \nabla  (\phi)\times \nabla  ( \psi) is different from the null vector field.

    Regards.

    Fernando Revilla
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  3. #3
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by FernandoRevilla View Post
    If \nabla  (\phi)=(2x,2y,2u) and \nabla  ( \psi)=(0,0,1) then, \nabla  (\phi)\times \nabla  ( \psi)=(2y,-2x,0) and this means that \nabla  (\phi)\times \nabla  ( \psi) is different from the null vector field.

    Regards.

    Fernando Revilla
    ok, I think I know where you got it from. Can you check i derived it properly? See attached. Thanks
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  4. #4
    A Plied Mathematician
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    Looks good to me.
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