Vector Equations - Concurrent Lines

[Peter G.]

Hi,

I have the equation to the path of two airplanes. They fly at the same height and I found the point where their paths intersect. The question says that the two planes do not collide and I have to prove so.

What I did was:

Airplane 1: (16 12) + t (12 -5)
Airplane 2: (23 -5) + t (2.5 6)

If (16 12) and (23 -5) are their starting points and the magnitude of (12 -5) (2.5 6) are their speeds I should be able to prove that they cross the intersection point at different times, thus, do not collide. My only doubt is if what I mentioned above is in fact their starting points. Are they?

Thanks,
Peter G.

 

[Pi-Bond]

You can say they are the starting points, as that is the position at t=0. It suffices to show that the x and y coordinates of the planes are same at different times (as you must have done.)