Final answer:
The internal jugular veins are the blood vessels that drain the brain and deeper areas of the head and neck, and they empty into the subclavian veins.
Step-by-step explanation:
The blood vessel that drains the head and neck on each side is the internal jugular vein.
Blood from the brain and the superficial facial vein flows into each internal jugular vein, which primarily drains blood from the brain and receives the superficial facial vein before emptying into the subclavian vein. Meanwhile, blood from the more superficial portions of the head, scalp, and cranial regions, including the temporal vein and maxillary vein, flow into each external jugular vein. The external jugular vein then leads to the subclavian vein. Both the internal jugular vein and external jugular vein ultimately contribute to the venous drainage of the head and neck, but it is the internal jugular vein that directly drains the brain and the deeper areas of the face and neck.