Where did this come from??? (3)
This is the same rotation matrix we saw earlier
It’s orthogonal and has determinant 1, so it must be a pure rotation.
It leaves the vector (X,Y,Z)T invariant, so it must be around that axis.
To find the angle, consider a rotation purely about X and use the half-angle formulas from trig.
Note that it’s double-valued: two quaternions give the same rotation.
The final result: a rotation about (X,Y,Z)T by an angle Q can be represented as the quaternion: