I.10.34 Flux of the vector field

( underline{mathrm{y}_{ ext {word: }}} ) Given a vector field ( vec{a} ) and a plane ( sigma ) intersecting the coordinate planes along a broken line ( K L M K ), where ( K, L, M ) are the points of intersection of the plane ( sigma ) with the axes Ox, Oy, Oz, respectively. 1) Find the flux (Q) of the vector field (vec{a}) through the part (S) of the plane (sigma), located in the first octant, in the direction of the normal (vec{n}), forming an acute angle with the axis (O z). 2) Find the circulation ( C ) of the vector field ( vec{a} ) along the contour ( K L M K ) formed by the intersection of the plane ( sigma ) with the coordinate planes. [ vec{a}=3(3-1) vec{imath}+(x+y-z) vec{k}, quad sigma: x+3 y+3 z=6 ]