# I Rotation matrix in 3x3

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1. Nov 1, 2016

### Silviu

Hello! I need to find the rotation matrix around a given vector v=(a,b,c), by and angle $\theta$. I can find an orthonormal basis of the plane perpendicular to v but how can I compute the matrix from this? I think I can do it by brute force, rewriting the orthonormal basis rotated by $\theta$ and doing some matrix multiplications, but is there a more clever and fast way to do it?
Thank you!

2. Nov 1, 2016

### Erland

I don't think there is any simpler method than "brute force".

3. Nov 1, 2016

### Filip Larsen

You might want to research Rodrigues' rotation formula.

4. Nov 1, 2016

### mathwonk

I guess this is what you are saying but the obviopus way to prceed seems to me to use the basis you have as a map sending the usual orthonormal basis to the new one, and use that map and its inverse to conjugate the (easily written) rotation about the z axis back to your axis.

5. Nov 3, 2016