The opposite of explicit is implicit. Something is explicit when it is stated in words. Something is implicit when it is not stated, but we are expected to understand it anyway. 

"Can we go to the museum tomorrow?"

Implicit: "The museum is closed on Mondays."

Explicit: "No, because tomorrow is Monday and the museum is closed on Mondays."

The opposite of precise is vague:

"Can we go to the museum tomorrow?"

Vague: "I think they close one day a week, don't they?"

Precise: "The museum is closed on Mondays."

Precise means that whatever is said is exact, clear, sharp, and well delineated.

Explicit means that what is said is complete, and that we actually say everything we want our listener to understand.