3. What do you think the relationship between the old man and the narrator is? What could have been the reason for the old man's "vulture eye"?

The old man and the narrator seemed to at least know or be acquainted with each other.

The cause of the eye is not specifically mentioned or revealed by the narrator but it is most probable that the old man got it as a result of an accident.

Explanation:

Edgar Allen Poe's short story "The Tell-Tale Heart" revolves around the story of the unnamed narrator insisting on his sanity after killing an old man. He had blamed the murderous act as something that the old man wanted, insisting that he did what he thought the old man wanted.

The relationship between the narrator and the old man seems to be that they know each other. This can be known from the narrator's statement that "And every morning I went to his room, and with a warm, friendly  voice". So, they knew each other.

When the narrator comments that the old man had "vulture eyes", he is describing the eyes of the old man. They looked like "the eye of one of those  terrible birds that watch and wait while an animal dies, and then fall  upon the dead body and pull it to pieces to eat it." And while the narrator did not delve into how the old man got the "vulture eyes", it may probably be that he got it from an accident, replacing his damaged eye with that of the "vulture eyes".

And that was the only reason he had ever wanted to kill the man, declaring "I did not hate the old man; I even loved  him. He had never hurt me. I did not want his money."

fearlessness is your answer

the objective should be switched