Where was David decapitated: chamber or ship?

same room, but not in the same place. I think he changed his position, but i dont have sure

David was decapitated in the "same" room, same position, after asking the engineer Weyland's question.

David was decapitated in the engineer ship. Once the ship crashed and Shaw dodged the octopus alien and pissed engineer she returned to the engineer's damaged ship to retrieve David. If you remember she lowered him down out of the ship once she put his head in the bag.