I.10.29 Flux of the vector field

Condition: Find the flow of the vector field \( \vec{a}=\alpha \vec{\imath}+\beta \vec{\jmath}+\gamma \vec{k} \quad \) through part of the sphere \( x^{2}+y^{2}+z^{2}=R^{2}, \quad \) located in the first octant. \[ \alpha=-2 x, \quad \beta=y, \quad \gamma=-2 z, \quad R=7 \]