I.10.13 Flux of the vector field

Calculate the flow of the vector field \( \vec{a}=3 x \vec{\imath}-z \vec{\jmath} \) through the closed surface using the Gauss-Ostrogradsky formula: \[ S: z=6-x^{2}-y^{2}, \quad z^{2}=x^{2}+y^{2}(z \geq 0) . \]