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Math Help - Vector Function

  1. #1
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    Vector Function

    determine the values of  a,b,c such that the vector vield

    F = (2x +ay -3z)i +(4x-y-bz)j +(cx-3y+z)k

    is irrotational i.e. \nabla \wedge F =0

    my attempt

    \nabla \wedge F = (-3+b) +(-3-c) +(4-a) = 0

    which is simplified to
    b-c+a =2

    what other formulas can i use to find a,b,c?
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  2. #2
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    Quote Originally Posted by iLikeMaths View Post
    determine the values of  a,b,c such that the vector vield

    F = (2x +ay -3z)i +(4x-y-bz)j +(cx-3y+z)k

    is irrotational i.e. \nabla \wedge F =0

    my attempt

    \nabla \wedge F = (-3+b) +(-3-c) +(4-a) = 0

    which is simplified to
    b-c+a =2

    what other formulas can i use to find a,b,c?
    Actually, what you want is \nabla \times F =0

    so

    \nabla \times F = <-3+b,-3-c,4-a> \,= 0 which gives a = 4,\, b = 3,\, c=-3.
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