These homophones have very different meanings and uses.

Right means correct, or opposite of left. It can be a noun, adjective, verb or adverb.

     Example: Turn right at the next corner.

The noun rite is a ritual, formal ceremony or religious practice.

     Example: Graduation is a rite of passage

Write is a verb meaning to compose or form letters or words.

     Example: I am going to write a letter.