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Math Help - Rotational and divergent

  1. #1
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    Rotational and divergent

    Calculate the rotational and divergent from each field below and say which are conservative.

    a) F(x,y,z)=(x+y,y-x,xz)

    b) F(x,y,z)=(x-2z,x+y+z,x-2y)

    c) F(x,y,z)=(e^xsiny,e^xcosy,z)
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    Calculate the rotational and divergent from each field below and say which are conservative.

    a) F(x,y,z)=(x+y,y-x,xz)

    b) F(x,y,z)=(x-2z,x+y+z,x-2y)

    c) F(x,y,z)=(e^xsiny,e^xcosy,z)
    Just use the formulas!

    Let \nabla = \tfrac{\partial}{\partial x}\bold{i} + \tfrac{\partial}{\partial y}\bold{j} + \tfrac{\partial }{\partial z}\bold{k}.

    Then, \text{div} (\bold{F}) = \nabla \cdot \bold{F} and \text{curl}(\bold{F}) = \nabla \times \bold{F}.

    It is conservative if it a fan of Pat Robertson, just joking, it is conservative if the curl is the vector zero.
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