Vapor on slanted bath ceiling with tile & skylight

Vapor barrier on slanted bath ceiling with tile & skylight

The bath we are enlarging has a slanted ceiling on one end of the room. The bathtub sits in an alcove below this ceiling area. We are putting in a skylight over the tub (30 x 30). I ordered a deck mounted skylight since the ceiling is slanted. This is a 100 year old farmhouse. The slanted part of the ceiling is lathe and plaster - pulled down the plaster where the skylight will be. I'm thinking I should take down all that plaster since it is so old and put up tile backer board and tile the ceiling same as around the tub. Should I put a poly vapor barrier on this ceiling? I bought the strongest exhaust fan I could find for this room. There is no heat vent in this room so we put in a heated tile floor for heating. That is why we wanted the skylight, to open for ventilation in summer since there is no cental air or window in the room. Is tile okay or any better ideas on how to finish the ceiling other than tile? The rest of the room has high ceilings with new flat finished drywall (no texture).

Thanks.