Question: Is there a vector field G on 3 such that curl G = x sin ( y ) , cos ( y ) , 4

Is there a vector field G on 3 such that curl G =
x sin(y), cos(y),4z xy
?
Step 1
We know that for any vector field
G = P i + Q j + R k
where P, Q, and R all have continuous second order partial derivatives, we must have
div(curl G)=.

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