So
P.Q = (1.7) + (2.-1) + (2.-1) = 7 - 2 - 2 = 3
P.R = (1.3) + (2.0) + (2.8) = 3 + 16 = 19
Q.R = (7.3) + (-1.0) + (-1.8) = 21 - 8 = 12
I believe the most likely situation is that the question or your information is wrong
Show that the triangle with vertices P(1,2,2), Q(7,-1,-1) and R(3,0,8) is right-angled.
My notes tell me that a triangle is only right angled if p.q = 0, but p.q = -11, p.r = 19, q.r = -29. I also tried to find out the individual angles and I got PQ = 120, PR = 42, QR= 118.
Am I making an obvious mistake or just doing something stupidly wrong? Thanks for your help :]