Thank you for the help!
"When I solved equations 2 and 3 I got u=0 and t=-1, giving me r = (-2,-3,0) in both r = ... equations."
Ok I'll check that. I just have a question...how would you get r = (-2,-3,0) when u = 0 and t = -1?
in r = (1,-1,1) +t(3,2,1) when t=-1
r = (1,-1,1) + (-3,-2,-1) = (-2,-3,0)
in the second r = (-2,-3,0) + u(1,2,3), when u=0
r = (-2,-3,0) + (0,0,0) = (-2,-3,0)