Fallout – How to get past the hologram room in the Sierra Madre Vault

Quick Walkthrough on how to get through the third floor and into the Vault (I think this is what you're looking for):

From the doorway where you enter this room, on the opposite side of the room, there's a long enclosure that runs most of the length of the opposite wall, plus a very small enclosure in the right corner. The doorway to exit this room is between these 2 enclosures, and one of the holograms is standing guard next to it.

There's also a medium-sized enclosure on the far-right wall that has a terminal that controls the Hologram next to the exit. Also, on your right as you come into the room, there's stairs going down to a lower catwalk level. The Cloud is covering this lower catwalk level, and you have to jump from the bottom of the stairs to the next section of this catwalk.

Also note the metal supports overhead. The hologram emitters are on top of the supports, but walking on them can be a little tricky, especially when the holograms turn hostile and start shooting you after you take out any of the emitters. To get to the overhead supports, jump on top of the far-right enclosure from the main catwalk. There's steps leading up to the supports from the top of the enclosure.

As you turn the corner after exiting the hologram room, your collar will start beeping as you run toward a speaker on the wall ahead of you.

This terminal lets you deactivate the weapon turrets and the blue forcefields around the Vault, allowing you to get into the Vault. But deactivating the security also triggers the entire sequence of events leading up to the confrontation with Elijah, including locking the elevator out of here until Elijah actually comes down to the Vault. So, switching off the security is basically a point of no return.

You'll see 2 folders regarding the Vault's security. Back out of the folder and you'll now see a 3rd option to disable the Vault's security protocols.