I. 12.14 Vector Field Circulation

Condition: Calculate by the Stox formula and directly circulation of the vector field \ (\ vec {a} \) along the contour G, indicating the direction of bypass on the drawing. \ [\ begin {array} {l} \ vec {a} = x^{2} \ vec {\ Imath}+y (z-2) \ vec {\ jmath}+(z+x) \ vec {k}, \\ \ Gamma: \ Left \ {\ Begin {Array} {l} x^{2}+y^{2} = 4 \\ x+y+z = 2 \ End {Array} \ Right. \ end {Array} \]