Let the position of two particles be given by r1 = {t,sin(t], cos(t)} and r2 = (t, 0,1]. (a) Describe any intersections of the curves described by the particle. (b) Describe any collisions between the particles themselves. (c) Repeat parts (a) and (b) but for particle positions r3 = (t 1,sin(t),cos(t)) and r4 = (t, (l, 1}, and discuss any differences in this case