Final answer:
In the Iliad, the gods play a significant role in determining the fate of Hector, as it is through divine intervention that Achilles is able to kill him. Artifacts like Exekias's amphora and Greek tragedies further illustrate the ancient Greek belief in the gods' substantial influence over human destiny, despite human attempts to shape their own fates.
Step-by-step explanation:
The gods in the Iliad by Homer don't directly speak about Hector's death as Achilles chases Hector, but their involvement throughout the epic suggests that they manipulate and influence the lives and fates of the mortal characters extensively. For instance, it is with the help of Athena that Achilles is able to kill Hector, indicating that without divine intervention, events might have taken a different course. This reflects a broader theme in the Iliad and Greek mythology where the role of the gods is pivotal, often determining the outcomes of human endeavors despite human efforts and desires.
The interaction between the divine and the mortal is also highlighted in artifacts such as the amphora depicting Achilles and Ajax, showing that the gods' influence was a well-accepted concept in ancient Greek culture. Furthermore, the amphora, crafted by Exekias, does not only illustrate a scene from daily life in a camp but also embodies the thematic essence of fate and the gods' role in it. The detailed throw of the dice that Achilles and Ajax make during their game in the artwork reflects the predetermined nature of their fates, one that is monitored and sometimes controlled by the gods.
The stories told in Greek tragedies by Sophocles and Euripides also emphasize the impact of the divine on human lives, where characters often find themselves at the mercy of the gods' wills, even as they grapple with their individual responsibilities and consequences of their actions.