Hey uglybdavis, that's a good start to what I need!
My question would be how to involve the second plane.
For instance, I have plane1, which is the plane of the existing triangle, and the 3 points of the triangle...
...Then I have plane2, which is the plane I want the triangle rotated into (remember, I want to retain the shape of the triangle).
How would you go about converting those points from plane 1 to plane 2? Pseudocode would be most welcome!