When you go into Vault 87 you must enter through Camp Little Light's cave system because the vault door entrance has 500+ rads per sec around it. However, even if you do get to the entrance to Vault 87, the door will never open even with Lockpicking 100; because it is labeled as impossible. If you enter through Camp Little Light and go into Vault 87, find the room where you see the back of Vault 87's door. Go to the yellow box (as you did in the prelude of the game, when escaping from Vault 101) to open Vault 87's. When it opens, you will see a gas-like wall of mainly a brownish color. When you walk through it, you will be teleported to the middle of Vault 87. Therefore, you can never walk between the outside door and the cog-like door of Vault 87. You will always be teleported back to the middle of Vault 87.