Unit vector (rot) between parent and child

Hello, I'm trying to get a unit vector representation of the rotation between a child and its parent (using the parent's +Z as reference axis).

The way I'm currently doing it is: childTransform.localRotation * parentTransform.forward;

Is this the correct way? Also, how can I reverse-engineer this so that, given a parent, a child and a unit vector, can I get the angles this unit vector represents?

Thank you very much! :)