#6. One the following vector fields F(x,y,z)= xyz*i +x²z*j+4x²yz³k G(x, y,z)=i+ (sin z) j + y (cos z) k is conservative and other is not. (a) Determine whether F is conservative or not. (b) Determine whether G is conservative or not. (c) For the vector field that is conservative find a function f such that the vector field is equal to Vf.

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#6. One the following vector fields
F(x, y,z)= xyz*i+x²z*j+4x²yz°k
G(x,y,z)= i+ (sin z) j+ y (cos z)k
is conservative and other is not.
(a) Determine whether F is conservative or not.
(b) Determine whether G is conservative or not.
(c) For the vector field that is conservative find a functionf such that the vector field is equal
to Vf.
Transcribed Image Text:#6. One the following vector fields F(x, y,z)= xyz*i+x²z*j+4x²yz°k G(x,y,z)= i+ (sin z) j+ y (cos z)k is conservative and other is not. (a) Determine whether F is conservative or not. (b) Determine whether G is conservative or not. (c) For the vector field that is conservative find a functionf such that the vector field is equal to Vf.
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