Vector Valued Function Spaceship Problem

[Baumer8993]

Homework Statement

The position function of a spaceship is r(t)= < 3+T, 2+ln(T), 7 -(4/T²+1)> , and the coordinates of a space station are (6, 4, 9). The captain wants to coast into the space station. When should the engines be turned off?

Homework Equations

I took the derivative of the position function to get the velocity function:
V(t)= <1, (1/T), (8T)/(T²+1)²

The Attempt at a Solution

Right now I have a vector I called U =<6-3+s>, 4 -(2+ln(s)), 9-[7-(4/s²+1)]
I got this hint from my professor. I understand that this is the position vector to the spaceship at time s. I know I now need to find the velocity vector that is parallel to the position vector. My professor gave me the hint to multiply by a constant K in the velocity vector function. At that point I would have two equations, and two unknowns which is easy to solve. I am just stuck on when I multiply by the constant K what would I set the velocity vector function equal too?

 

[clamtrox]

When the engines are switched off, the spaceship will probably move in a straight line. So you want to switch them off when your velocity vector points from r(t) towards the space station.

 

[LCKurtz]

This is a repost of

https://www.physicsforums.com/showthread.php?t=667299

Why are you reposting a question that has already been replied to?