Final answer:
The axillary vein is formed by the union of the brachial and basilic veins. The basilic vein travels medially and superficially through the arm, while the brachial vein is formed by the radial and ulnar veins and lies deeper.
Step-by-step explanation:
The vein formed by the union of the brachial and basilic veins is known as the axillary vein. The basilic vein is a superficial vein of the arm that arises from the palmar venous arches. As it travels through the arm, it remains medial and superficial up to the antecubital region, where it intersects with the median cubital vein, and then continues into the upper arm. On the other hand, the brachial vein is a deeper structure that forms from the union of the radial and ulnar veins. Together, the basilic vein and the brachial vein lead to the formation of the axillary vein.