If you are drilling a hole through 3 pieces, and you do not want to purchase a 12" "twist" (metal bit) bit to do the job, which would be the way to do it.
If you choose to use the shorter version, there is a way to do that too. Main thing is, is to use a twist bit since it is full round so to speak and once it starts in a direction, it usually will not redirect or change it's angle of drilling. It will take a few steps to accomplish the job.
First drill the hole all the way in as far as it will possibly go, hopefully a good distance into the second piece. If possible re-chuck the drill bit into the drill so it is barely in the chuck to maximize the drill depth, after you do the initial fist bore to get that "last little bit of depth".
Remove the first piece you drilled through. Using the hole that is started in the second piece, and re-chucking the drill bit in properly continue drilling using the hole that was started in the second piece as a guide. If that does not get you all the way through, use the same method mentioned earlier to get the rest of the way through.
If the holes are needed to go through the 7 1/4" height of the beam, you would be wise to get the long drill bit. If not take the chance and line the holes from either side the best you can, drill them in as deep as possible from each side and hammer the livin' crap outta them. They might make through... I have been that fortunate doing it that way too. It does blow out the wood a little bit on one side. That is the trade off, if it works....
Sandwich the workpiece between two pieces of wood, clamp it all together, clamp the whole assembly so that it can't go spinning off into oblivion, then drill through the whole thing. You'll also want to use really light pressure when drilling through the plastic, but don't go so slow that you melt the stuff.
If you have some, you could use a step drill instead of a twist drill.
If you have a bunch of in between size bits, you can simply start small and slowly work your way up to the final size. However, you're still going to want to properly brace the material. Adding support behind the piece is also a good idea.
If it's within your budget, a drill bit designed to drill plastics might work. However, you're still going to have to secure the workpiece while drilling. I'd also recommend using a wood backer, to support the piece as you drill.
Best Answer
The Dremel will do what you need here. The 2nd bit from the left will work perfectly. It will drill a small pin hole to a larger hole the size of the largest portion of the bit