Precise and exact are synonyms - meaning that something is correct to the last detail. Accurate is a little bit looser - meaning that something is a very close to correct. It is used to discuss aim when someone is able to hit a target well. (You can think of it that way for when a person is trying to understand ideas, as well. They may not understand every facet correctly, but if they are close, then someone else might say, "That's pretty accurate.") "Veracious" is different in that it means "being honest." Rather than the level of detail that is paid attention to, it seems to be the level of truthfulness with this word.