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## Main Question or Discussion Point

Hey,

I am trying to solve the following problem:

I know the vectors

So there are 9 equations and 9 unkowns. But if I try to solve this problem analytically I can not come to any answer. I also put it in MATLAB but this also gives weird results.

My first attempt was subtracting the vectors which eventually gave me a solution for omega. But than I still could not solve the problem.

Does anyone know why this is the case? Is it something with the outer product which I don't understand? Are there infinite number of solution to this problem? Or do I just do something wrong?

Any help would be appreciated since I am already trying things for some days.

Thanks.

I am trying to solve the following problem:

**v**=_{a}**v**+_{r}**ω**×**r**_{ra}**v**=_{b}**v**+_{r}**ω**×(**r**+_{ra}**r**)_{ab}**v**=_{c}**v**+_{r}**ω**× (**r**)_{ra}+r_{ac}I know the vectors

**va**,**vb**,**vc**,**r**and_{ab}**r**and I want to know the angular velocity vector, the radius_{ac}**r**and the velocity_{ra}**v**. Physically it means that I know 3 points on a rigid body and I want to decompose their velocities in an angular and linear component by determing around which point they rotate._{r}So there are 9 equations and 9 unkowns. But if I try to solve this problem analytically I can not come to any answer. I also put it in MATLAB but this also gives weird results.

My first attempt was subtracting the vectors which eventually gave me a solution for omega. But than I still could not solve the problem.

Does anyone know why this is the case? Is it something with the outer product which I don't understand? Are there infinite number of solution to this problem? Or do I just do something wrong?

Any help would be appreciated since I am already trying things for some days.

Thanks.