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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.