Suppose that after t seconds, where t≥ 0, the trajectories of two particles are given by the vector functions r₁(t) = (t², 15-4t, 1²), r₂(t) = (4t-3,t(4-t), 2t+3) (a) At what point do the two particles collide? That is, at what point is r₁(t) = r₂(t) for the same value of t? (b) Find their angle of collision, correct to the nearest degree. (c) Do the two trajectories cross paths anywhere else? That is, is there s,t> 0 such that s t and r₁(t) = r₂(s)? If so, find all such points. If not, explain why not.

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