The important part about the orthogonal plane is that when you rotate it, all pairs of points that were in the orthogonal plane before are still in the orthogon

The important part about the orthogonal plane is that when you rotate it, all pairs of points that were in the orthogonal plane before are still in the orthogonal plane. Same thing is true of the axis of rotation. All other pairs of points will be in a different plane than they were before the rotation.