i.12.5 Vector field circulation

Calculate the circulation of the vector field \( \bar{a} \) through the closed loop \( L \) directly and using the Stokes formula: \[ \vec{a}=x y \vec{\imath}+y z \vec{\jmath}+z x \vec{k}, \quad L:\left\{\begin{array}{l} x+y+z=1 \\ x=0, y=0, z=0 \end{array} .\right. \]