I.10.34 Flux of the Vector Field

(Underline {Mathrm {Y} _ {Ext {Sliding:}}}) The vector field is given (Vec {a}) and the plane (sigma), crossing the coordinate planes along the broken (k l m k), where (k, l, m) the intersection points of the plane (sigma) with axes OX, OY, OZ, respectively. 1) Find the flow (q) of the vector field (Vec {a}) through the part (s) of the plane (sigma), located in the first octant, in the direction of normal (Vec {n}), forming an acute angle with an 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 coordinate planes. [ vec {a} = 3 (3-1) vec {iMath}+(x+y-z) vec {k}, quad sigma: x+3 y+3 z = 6 ]