I.10.27 Flux of the Vector Field

Condition: Find the flow of the vector field \ (\ vec {a} = (x-2 z) \ vec {\ iMath}+(x+3 y+z) \ vec {\ jmath}+(5 x+y) \ vec {k} \) through the upper side of the triangle \ (a b c \), cut off coordinate coordinate planes from the plane \ (\ alpha x+\ beta y+\ gamma z = 1 \). The problem is solved in two ways: ordinary and through projections. \ [\ Alpha = -3, \ Quad \ Beta = 2, \ Quad \ Gamma = 4 \]