(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1.

Calculate:

[tex] \nabla \times (\frac{\vec{p} \times \vec{r}}{r^{3}})[/tex]

in cartesian and spherical coordinates, where [tex] \vec{p}[/tex] is a constant vector.

2.

Calculate surface integrals:

[tex] \int \vec{r} (\vec{a} \cdot \vec{n}) dS[/tex]

[tex] \int \vec{n} (\vec{a} \cdot \vec{r}) dS[/tex]

where [tex]\vec{a}[/tex] is a constant vector and [tex]\vec{n}[/tex] is a unit vector normal to the surface.

2. Relevant equations

3. The attempt at a solution

I tried do the first by using some basic vector identities but I didn't get anywhere (the result wasn't by any means neat and short ;)). I was told that Dirac delta is supposed to show up somewhere, but I don't see it.

The second one is probably done using Stokes' Theorem but I don't see any simple fashion in which it can be applied.

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# Homework Help: Vector identities

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