(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For what value(s) of the scalar 'a' is the vector field

F(x,y,z)= 2xz i + ay^3 j + (x^2 + y^4) k conservative

3. The attempt at a solution

F1=2xz

F2=ay^3z

F3=(x^2 + y^4)

I used 3D curl test??

1)(partial F2)/(partial dx) - (partial F1)/ (partial dy)= 0-0 = 0

2)(partial F3)/(partial dy) - (partial F2)/ (partial dz)= 4y^3 - ay^3=0 so a=4

3)(partial F1)/(partial dz) - (partial F3)/ (partial dx)= 2x-2x = 0

my answer would be a=4

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# Homework Help: Vector field, Conservative?

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