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Answer by Calvin Khor for How to Find The outward Normal Vector in this case

It is (i) that is correct, not (ii). This is because it is part of the surface of the sphere. It is constrained to lie inside the cyllinder, but this doesn't mean that the surface is part of the...

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Answer by user for How to Find The outward Normal Vector in this case

The outward normal vector for the sphere is $$\vec n =\frac1{\sqrt{x^2+y^2+z^2}}\left(x,y,z\right)$$ Note that the sphere and the cylinder have in common the circle in the $x-y$ plane therefore $S$...

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How to Find The outward Normal Vector in this case

So, here is the question : Find $\displaystyle \int\int_{S} \text{curl F}ds$ where $\vec{F} = xz\hat{i} + yz\hat{j} + xy\hat{k}$ and $S$ is the part of the sphere $x^2 + y^2 + z^2 =1$ that lies inside...

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