Problem 1. If two objects move through space along dierent trajectories, typical

Question

Problem 1. If two objects move through space along dierent trajectories, typically it is

benecial to know whether these objects collide (for example, you probably do not want

cellular satellites to collide but you do want NASA's crew to successfully land a nuclear

bomb on part of a Texas-sized asteroid in the hit 1998 lm Armageddon).

Suppose the trajectories of two objects are given by the vector functions

~r1(t) = ht2; 7t ?? 12; t2i

~r2(t) = h4t ?? 3; t2; 5t ?? 6i

for t 0.

Do these objects collide? If so, at what time and what position (i.e. what 3D coordinate)

do they collide?

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