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### Verify Stokes' theorem for $F=2yzi-(x+3y-2)j+(x^2+z)k$ where $S\subset \mathbb{R}^3$

Please note that at the intersection of both surfaces, $x^2 + y^2 = x^2 + z^2 \implies y = z$ Surface $x^2 + y^2 = a^2$ should be parametrized as, $\phi(z, t) = (a \cos t, a \sin t, z)$ with normal ...
• 50.6k

### Intuition behind curl identity $\nabla\times (\nabla\times A)=\nabla (\nabla \cdot A)-\nabla ^2A$

How could one explain this result in intuitive terms? One heuristic way is to treat the operator $\nabla$ formally as a vector and think about the Lagrange formula for the triple cross product of ...
• 2,385