I.10.20 Flux of the vector field

Condition: Find the field flux \( \vec{a} \) through the surface \( S \) : \[ \begin{array}{l} \vec{a}=2 x y \vec{\imath}+4 y z \vec{\jmath}+y^{2} \vec{k} \\ S:\left\{\begin{array}{c} x+3 y+6 z=6 \\ x \geq 0, \quad y \geq 0, \quad z \geq 0 \end{array}\right. \end{array}\]