I.10.18 Flux of the vector field

Condition: Let \( \sigma \) be the part of the plane \( P \) limited by the coordinate planes, and \( \sigma_{0}- \) be the complete surface of the pyramid resulting from the intersection of the plane \( P \) and the coordinate axes. Calculate: a) Field flux \( \vec{F} \) through the surface \( \sigma \), b) Field flux \( \vec{F} \) through the surface \( \sigma_{0} \) directly, c) Field flux \( \vec{F} \) through the surface \( \sigma_{0} \) according to the Gauss-Ostrogradsky formula, \[ \vec{F}=(2 x+5 y+2 z) \cdot \vec{k}, \quad P: x+y+3 z-6=0 \]