Homework #3 SolutionsMath 23, Fall 20141.Suppose two particles travel through space, with their positions given by thevector functions~r1(t) =2t, t2, t+ 2and~r2(t) =2(t-2)2,8t-16,2t-2.(a)Do the paths of the particles (that is, the space curves they move along)intersect? If so, find the points of intersection.
(b)Do the particles collide? If so, when and where?