i.12.3 Vector field circulation

condition: Calculate the circulation of the vector field \( \bar{a} \) through a closed contour L, which is the intersection of given surfaces, directly and using the Stokes formula: \[ \vec{a}=y \vec{\imath}-x \vec{\jmath}+z \vec{k}, \quad \text { L: }\left\{\begin{array}{c} x^{2}+y^{2}+z^{2}=4 \\ z^{2}=x^{2}+y^{2} \end{array}\right. \]