A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is

. We have

so this vector field is not conservative.
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Another way of determining the same result: We want to find a scalar function

such that its gradient is equal to the given vector field,

:

For this to happen, we need to satisfy

From the first equation, integrating with respect to

yields

Note that

*must* be a function of

only.
Now differentiate with respect to

and we have

but this contradicts the assumption that

is independent of

. So, the scalar potential function does not exist, and therefore the vector field is not conservative.