Final answer:
The splenic vein is the vessel that runs along the posterior surface of the body and tail of the pancreas, responsible for draining blood from the spleen and pancreas into the hepatic portal vein.
Step-by-step explanation:
The vessel that courses along the posterior surface of the body and tail of the pancreas is the splenic vein. The abdominal aorta after crossing through the diaphragm at the aortic hiatus becomes known as the abdominal aorta. From here, several key branches arise to supply various parts of the abdomen with blood. The celiac trunk is one of the major branches of the abdominal aorta, and it gives rise to the left gastric artery which supplies the stomach and the esophagus, the splenic artery which supplies the spleen, and the common hepatic artery which forms the hepatic artery to the liver, the right gastric artery to the stomach, and the cystic artery to the gallbladder. However, of all vessels listed, the one that runs posterior to the pancreas is the splenic vein, which is responsible for draining blood from the spleen and pancreas and delivering it into the larger circulation system via the hepatic portal vein. The correct answer to the question is thus E) Splenic vein.