Is this a good place to get help with Calculus II problems? I am seriously failing....
I would do it this way:
Find the distance between P&Q, Q&R, and R&P (this should be easy enough, let me know if you need help there is a formula for distance between points in 3 dimensions)
Now you have 3 sides of the triangle. According to Euclid's SSS proof their is only one possible triangle given three sides.
Now you can use sin or cos to figure out the angle PQR which is the one most likely to be a right angle.
Let me know if you need further help.