Two particles travel along the space curves:
(a) Do the particles collide?
(b) Do their paths intersect?
For the two particles to collide, there must be a value of t such that r1(t) = r2(t). So, I set the components of the positions functions equal to each other:
t = 1 + 2t => t = -1
t^2 = 1 + 6t => t = 3 + or - sqrt(10)
I can see already that because t is equal to different quantities in the first two components, the particles do not collide.
I'm not sure how I might find if the space curves ever intersect...Other than using the same method I used above, which just can't apply for both parts.
Thanks for any responses!