Evaluate $\int_S F.n dS$ where $F=18zi-12j+3yk$ and S is the part of the plane $2x+3y+6z=12$ which is located in the first octant.
Here div $F=0$ so by Gauss divergence theorem value of the integral is 0.
I have doubt about the answer. Am I right?
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Try computing $F \cdot n$ with the outward pointing normal as $(x \mathbf{i}+y \mathbf{j}+z \mathbf{k})/(x^{2}+y^{2}+z^{2})^{1/2}$ and you may get another answer... – Autolatry Mar 10 '15 at 16:31