Final Answer:
The maxillary artery sits on top of the pterygoid muscles and is located under the maxilla bone.
Step-by-step explanation:
The maxillary artery is one of the major branches of the external carotid artery. It enters the deep face by passing through the infratemporal fossa, which is a space situated below the base of the skull. In this anatomical region, the maxillary artery is positioned on top of the pterygoid muscles, specifically the lateral and medial pterygoid muscles.
These muscles are part of the masticatory apparatus involved in jaw movement. The maxillary artery then continues its course within the pterygomaxillary fissure, which is a cleft between the maxilla and the greater wing of the sphenoid bone.
Therefore, the maxillary artery is situated on top of the pterygoid muscles and is located under the maxilla bone.