9.9.2 Potential and solenoidal fields

3) Problem: Show that the field \( \vec{a} \) is potential and find its potential: \[ \vec{a}=\left(\frac{y}{z}+2 x\right) \vec{\imath}+\frac{x}{z} \vec{\jmath}-\frac{x y}{z^{2}} \vec{k} . \]