For each of the following vector fields, determine whether a vector potential exists. If so, find one.
For this problem, enter your vectors with angle-bracket notation: $<a, b, c>$, not in $ijk$-notation.

(a) $\vec F = 2x\,\mathit{\vec i}+\left(5y-z^{2}\right)\,\mathit{\vec j}+\left(2x+7z\right)\,\mathit{\vec k}$
$\vec F$ ? has a vector potential does not have a vector potential $\vec H$, $\vec H =$
(If there is no potential function, enter none for the function.)

(b) $\vec F = 2x\,\mathit{\vec i}+\left(5y-z^{2}\right)\,\mathit{\vec j}+\left(2x-7z\right)\,\mathit{\vec k}$
$\vec F$ ? has a vector potential does not have a vector potential $\vec H$, $\vec H =$
(If there is no potential function, enter none for the function.)