Tracking a Space Ship: Will an Asteroid Hit the Target?

[mjbourquin]

This problem is a sample flight path of a ship in space.
Its path is described by the line r(t) = (-1+t)i + (2-t)j
An asteroid has the starting point (0, 5, -1) and a heading vector of 2i + j + 3k
Ship
x = -1 + t
j = 2 -t
z = 0

asteroid

x = 0 + 2t
y = 5 + t
z = -1 + 3t

The question is will the asteroid hit the ship and if not how close will they come.

 

[D H]

We do not do your homework for you at this site. We help you do your own homework. Before we can even start offering help you need to have shown some work on the problem.

 

[mjbourquin]

I don't even know how to start. A hint in my homework states that if two lines do not intersect, they can be embedded in parallel planes but I don't know how that helps me find how close two lines come to each other. If they do intersect I would plug both lines into an r(t) and set them equal. Then find t. Is that right.

 

[D H]

Hint: What is the distance between the ship and asteroid at time t? What is the minimum of this distance?

 

[mjbourquin]

oh, I forgot all about optimization derivatives. Much easier. Thanks.