I.12.10 Vector field circulation

\( \underline{\mathrm{y}_{\text {word: }}} \) Let \( \sigma \) be the part of the plane \( P \) limited by the coordinate planes. Calculate the circulation of the field \( \vec{F} \) through the contour bounding the surface \( \sigma \) directly and using the Stokes formula. \[ \vec{F}=(2 x+5 y+2 z) \cdot \vec{k}, P: x+y+3 z-6=0 \text {. } \]