I noticed that my tub and vanity which are on the same outside wall attached to each other are pulling away from the wall, with about a 1/4 inch space or more on the vanity and a 1/8 inch or so gap downward from the recently redone caulk on the tub. The house is about 14 years old. Never used this tub much till now since there is also a standing shower. Always thought it was a little bit off, but since I've really started using it the last few weeks it is definitely pulling away. What do I need to do to fix this or identify the problem and what needs to be done. It is a 2 story with a walk out basement, with a steep backyard.

Something wrongs with the floor possibly. If the drainage lines in the joist were drilled wrong this could cause the "sag" effect that's creating the gap.
You say the tub and sick are attached to each other. Is there a portion Wall between the two?
How hot and cold does this room get in a 24 hr time in difference?
Any more detail in info could help here

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There is a small ledge between the two, a little shorter than the tub, the room is at a pretty constant temperature. The stand up shower is bordering the other side of the tub with a short ledge. The tub is in the corner against 2 exterior walls. It is not a standard tub but more circular in a roughly rounded triangular shape it is a taller tub with a step to enter the tub. Could water leaking from the shower weaken the floor it seems poorly calked at the end of the shower facing the tub between the window and the tile at tub level?

The joist was my next thought. If the tub trap is dripping without you knowing it that can soften the floor. Out it this way for anything to move its either the sink / tub / wall is moving and to cause that is movement of objects. I'm laughing at myself NO kidding 21 Boat ha!
So anyhow check the traps on tub and sink and all supply valves to see if the sub floor is getting wet report back Thanks!
Is there a crawl space below this room?

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