F two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions r1(t) = t2, 13t − 36, t2 r2(t) = 7t − 12, t2, 5t − 4

The two objects will collide with the same position vector for all three components at exactly t = 4 s

Explanation:

For two particles starting out at the same time to collide, their position Vector's at the time of collision must be exactly the same.

So, at the collision point, position vector of object 1 is equated to that of object 2.

r₁ = (t², 13t-36, t²)

r₂ = (7t-12, t², 5t-4)

At he point of collision

t² = 7t - 12

t² - 7t + 12 = 0

t² - 4t - 3t + 12 = 0

t(t - 4) - 3(t - 4) = 0

t = 3s or t = 4s

13t - 36 = t²

t² - 13t + 36 = 0

t² - 4t - 9t + 36 = 0

t(t - 4) - 9(t - 4) = 0

t = 9s or 4s

t² = 5t - 4

t² - 5t + 4 = 0

t² - 4t - t + 4 = 0

t(t - 4) - 1(t - 4) = 0

t = 1s or t = 4s

The three components intersect at other times, but at t = 4s, they all intersect at the same time! Meaning that, at this point the two objects are at the same place with the same position vector at that time.

first thing first of the answer is with technology. second thing second thing is that the big bang theory did not happened u see they say it did but what they dont realize is that like dinasures are still a round they might deny it but they and look at these 12 foot human skelteons they find lets see didnt the bible say something about giants. hope this peace.