PS plus across three consoles?

so , if i have a ps3 , am buyinng a vita and a ps4 will my ps plus work on all three consoles or what would be the deal with that? Im not sure if this has been brought up or not but i couldnt find any answers 

The same account already works accross a PS3 and Vita.  Can't imagine any situation where it won't also link up to a PS4.

Edit - Here we are. http://us.playstation.com/psn/playstation-plus/ 

"One membership, three devices

PlayStation®Plus members can carry their membership over to their PS4 system, and continue to use it with their activated PS3 and PS Vita systems, at no additional cost."

Of course it works