Two particles travel along the space curves r1(t) and r2(t), where t is the time.

r₁(t) = ti + t²j + t³k

r₂(t) = (-2t + 3)i + 8tj + (12t + 2)

A collision will occur at the point of the intersection P if both particles are there at the same time.

a. Do the particles collide?

b. Do their paths intersect?