Final answer:
Apollo's interaction with Achilles, particularly in the context of the Iliad, is crucial to Achilles' fate. Apollo guides the arrow shot by Paris to strike Achilles' only vulnerable spot, his heel. The tragic outcome of this interaction is central to the narrative of the Trojan War and its heroes.
Step-by-step explanation:
The interaction between Apollo and Achilles is one that stems from the rich tapestry of Greek mythology and is captured in various works of art, including that by Velázquez in 'Apollo in the Forge of Vulcan'. However, the primary interaction between Apollo and Achilles is detailed in Homer's Iliad, where Apollo plays a significant role in the events leading to Achilles' death.
Their direct interaction is most notable when Apollo guides Paris' arrow to strike Achilles at his one vulnerable spot, his heel, which ultimately leads to Achilles' death. The term 'Achilles heel' has henceforth been used to describe a person's point of greatest vulnerability. On the contrary, the amphora described depicts a moment of quieter interaction between Achilles and another Greek hero, Ajax.
It is through the artistic representation of artifacts like the amphora created by Exekias, and tales from the Iliad, that the complexities and fates of these legendary figures are conveyed.