Final answer:
The locking jaws of a tractor-trailer hitch should close securely around the shank of the king pin, the part just underneath its head, to ensure a safe connection between the trailer and the tractor.
Step-by-step explanation:
In the context of tractor-trailer rigs, the locking jaws should close around the shank of the king pin. The king pin is crucial in connecting the trailer to the tractor, and it is essential for the locking jaws to have a secure grasp on the shank of the king pin to ensure that the connection is safe and secure. It is the cylindrical part of the king pin, just underneath the head, where the locking jaws should engage.