i.12.i Vector field circulation

Condition: Calculate the circulation of the vector field \( \vec{F} \) through the closed loop \( L \) directly and using the Stokes formula: \[ \begin{array}{l} \vec{F}=a x^{2} y \vec{\imath}+y^{2} z \vec{\jmath}+x z^{2} \vec{k}, \quad L:\left\{\begin{array}{c} x^{2}+y^{2}+z^{2}=b^{2} \\ x=c \end{array}\right. \\ a=3, \quad b=2, \quad c=3 . \end{array}\]