i.12.8 Vector field circulation

Condition: For \( \quad \) vector field \( \vec{F}(x, y, z)=\left(x z, y z, z^{2}\right) \) calculate the circulation along the contour \( C \), where the closed contour \( C \) : \[ \left\{\begin{array}{c} y=z \\ y=2 z \\ z=1 \\ x=2 \end{array}\right. \]