Consider the twisted cubic r(t) = (t, t², t³) and the line r2(s) = (1+s, –1+5s, 1+7s). (a) Show that these two curves intersect at at least one point in R³. (b) One object starts moving along the twisted cubic in the positive direction, while a second object starts moving along the line in the positive direction. Both ob- jects start moving at the same time t = s = 0, each measured in seconds, at the respective starting points given by these curves when t = s = 0. Show that the objects NEVER collide. (c) Briefly explain why part (b) does not contradict part (a).