I have not understood this well, despite doing a lot of background reading.

I guess all of these vectors are being added only as projections along the same direction? So, a vector perpendicular to another would not change its value, parallel vectors would add, antiparallel vectors would subtract.

I don’t think I understand the concept very well, but this would mean:

J=2 –> parallel
J=1 –> perpendicular
J=0 –> antiparallel