My original intent in this discussion was to find out if it was even possible. When it comes to video, consider me like your great-grandfather who only understands the on-off-volume knob on a television set. if it's much more complicated than that it is out of my league. I have learned how to connect my laptop in the classroom, and considering that the Note 3 is pretty close to a real computer, I wondered if it might be possible to connect it as well.
Today I went to the AV Help Desk at the university and showed my Note 3 to the fellow at the desk and asked if it was possible to connect it to the overhead projectors in the classrooms. He immediately asked what classroom I needed to use it in, because apparently some classrooms have HDMI instead of VGA. I've never seen anything but VGA connectors in any of the classrooms I have used, so I told him I needed VGA.
He turned to a rack with various devices hanging on hooks that you can check out. He offered me a micro USB to VGA adapter that he thought would work with my Note 3. I suggested that maybe I'd be better off just to spring a few bucks and buy my own on Amazon. He immediately sat down at his computer, checked Amazon and found several, including one that apparently includes both a VGA and an HDMI adapter. So now I'm off to Amazon for shopping.
I'd still like to know if anyone here has actually successfully connected a Note 3 to an overhead projector and, if so, what adapter you used.