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Homework Statement
What is the sum of position vectors of all points on a circle? Don't use Cartesian system.
Homework Equations
Sum vector $$\vec s = \int_{\theta=0}^{\theta=2{\pi}}\int_{r=0}^{r=R} \, \,\vec P \, dr d\theta$$
where $$\vec P$$ is the position vector.
The Attempt at a Solution
Using latex proving extremely difficult, so I'll just post a pic.
What I don't want is to write the unit vectors in cartesian form and solve.
I must have done something wrong, because the s vector should point to the origin.
Please help.
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