I.10.29 Flux of the Vector Field

Condition: Find the flow of 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 \]