I have a 3d rigid body rotation under which the unit vector $(0, 0, 1)$ becomes the unit vector $(n_x, n_y, n_z)$. I need to find what the vector $(w_x, w_y, 0)$ transforms to under that same rotation. All help much appreciated.
2026-03-24 20:40:09.1774384809
Seeking 3d rotation
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A rotation can be described by an axis and an angle. To get the axis of rotation, just take the cross product of the initial and final state (I assume that $(n_x,n_y,n_z)\ne(0,0,\pm1)$), and then normalize the length to be $1$. The cross product and dot product will also give the angle of rotation.
Once you have these values, you can write the rotation matrix, according to this formula. Then just multiply the matrix with the $w$ vector.