Compute the flux of the vector field $\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented upward.
What is the answer if the plane is oriented downward?

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The Answer of Compute the flux of the vector field $\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented upward.
What is the answer if the plane is oriented downward?

Compute the Flux of the Vector Field F⃗=(x−4y)i⃗+(4y−2z)j⃗+6xk⃗\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }F=(x−4y)i+(4y−2z)j​+6xk

Compute the Flux of the Vector Field $\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }$