Final answer:
Blood from the external jugular vein drains into the subclavian vein, which then, along with other vessels, forms the brachiocephalic vein, ultimately leading to the superior vena cava.
Step-by-step explanation:
The blood in the external jugular vein drains into the subclavian vein. The subclavian vein is where the axillary vein from the arm region transforms when it passes through the body wall. This vein then fuses with both the external and internal jugular veins from the head and neck, contributing to the formation of the brachiocephalic vein. The brachiocephalic veins, which are paired structures, eventually carry blood to the superior vena cava, which then drains into the right atrium of the heart, completing the venous return from the upper part of the body.