I don't understand why the x direction force for TAB is 0 when it is in the x direction?
media.cheggcdn.com/media%2F272%2F2729fce3-76ed-4803-ad04-3638b6a8e4de%2FphpJ3gLHL.png
2 answers
the rope AB is in the y z plane. A rope can not pull sideways.
I see, you are assuming x is to the right. However look more closely. X is out of the paper toward you, y is to the right, and z is up.