Final answer:
The eccrine sweat glands are responsible for producing sweat during activities such as playing basketball, helping to regulate the body temperature through thermoregulation and maintaining homeostasis.
Step-by-step explanation:
The gland involved in creating sweat after playing a vigorous game of basketball is the eccrine sweat gland. These glands are responsible for thermoregulation by producing a hypotonic sweat that is released onto the skin's surface through pores. The eccrine glands are especially abundant on the palms, soles of the feet, and the forehead, and when the body becomes warm, such as during intense physical activity, they actively secrete sweat to cool the body down. The sweat produced by eccrine glands is mostly water but also contains salt, antibodies, traces of metabolic waste, and an antimicrobial peptide known as dermicidin, all of which help maintain homeostasis.