Can a Playstation 4 be used simultaneously while remote playing with a Vita?

I am interested in buying a PS4 and have a question related to remote play: If I were to remote play with the Playstation 4, could another person be playing it separately as well? For example, could I be streaming Need for Speed Rivals to my Vita, while say my brother plays Knack?

Obviously this couldn't be done with disc based games, but would it be possible to have two users doing different things simultaneously. Also, if this could be possible, would it allow to different PSNs to be logged in at the same time?

Solution 1:

No.

Only one user can use the system at a time.

While multiple users can be logged in, the Vita will display the same as the current view on the TV, and if the Vita user isn't the one with control (you get it from pressing the PS button on the Vita if another user has logged into the console), it can't do anything but watch.

You can't be signed into the same account on both.