Final answer:
The b.medulla oblongata houses the vital centers for regulating heart rate, respiratory rhythm, and blood vessel diameter, making it the correct answer.
Step-by-step explanation:
The vital centers for regulating heart rate, respiratory rhythm, and blood vessel diameter are in the medulla oblongata. The cardiovascular center within the medulla oblongata encompasses various nuclei that respond to changes in blood pressure and blood concentrations of gases through autonomic connections. Particularly, the cardioaccelerator nerves increase heart rate while the vasomotor nerves are responsible for the constriction of blood vessels.
In contrast, the hypothalamus serves as the master control for homeostasis through the autonomic and endocrine systems and is not directly responsible for the regulation of cardiovascular function. Hence, the correct answer to the student's question is option B) Medulla oblongata.