Undergrad Rotation Matrix for Vector v=(a,b,c) by Angle θ | Efficient Computation Method

[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!

 

[Erland]

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

 

[Filip Larsen]

You might want to research Rodrigues' rotation formula.

 

[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.

 

[jasonRF]

Sorry I missed this post earlier in the week. Here is a post that describes how to construct such a rotation and shows what the result should be:
https://www.physicsforums.com/threads/rotation-matrices-in-r-3.326037/#post-2285199

Jason