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Thread: Vector Function

  1. #1
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    Vector Function

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

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

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

    my attempt

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

    which is simplified to
    $\displaystyle b-c+a =2$

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

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

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

    my attempt

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

    which is simplified to
    $\displaystyle b-c+a =2$

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

    so

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