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for two vector fields F and G for which ∇xF= ∇xG can it be said in...

for two vector fields F and G for which ∇xF= ∇xG can it be said in general that F=G?
if answer is no, find the ? in the expression
F=G + ?
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for two vector fields F and G for which ∇xF= ∇xG can it be said in general that F=G? if answer is no, find the ? in the expression F=G + ?

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