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## Homework Statement

I need to evaluate this integral:

[tex]\int (\hat{r}\cdot\vec{a})\hat{r}d\Omega[/tex]

where [tex]\hat{r}[/tex] is the radial unit vector, [tex]\vec{a}[/tex] is a constant vector and [tex]d\Omega[/tex] is solid angle element ([tex]\sin\theta d\theta d\phi[/tex]).

I saw something similar, but it was with tensors, and mean values but that was puzzling enough :\

I tried looking at components, but I came to nothing smart. I have the answer ([tex]\frac{4\pi}{3}\vec{a}[/tex]).

Any hints?