# Thread: vectors distance and velocity - FP3

1. ## vectors distance and velocity - FP3

I am having difficulty with the following question cause i donn't understand the stuff about velociand am thus finding difficult to apply what the chapter has tought me about distances from a point to a line/plane,

The question:

Two ships are moving with constant, but different velocities v_1 and v_2.
At noon the ships have position vectors a_1 and a_2 respectively with respect to a fixed origin.
The distance b/w the ships is decreasing. Show that:

(v_1 - v_2).(a_1 - a_2)<0 (1)

The ship with velocity v_1 will sight the second ship if the distance b/w ships is at any times, less or equal to d, where d<|a_1-a_2|.
Show that sighting will occur provided

d^2 > or = to |a_1-a_2|^2-{[(v_1-v_2).(a_1-a_2)]^2/|v_1-v_2|^2}

for the first i see that since their velocities are different the first term in (1) will be different to zero, if it is negative then ship 1 will have the slowwest velocity and hence will be behind ship 2 and so the second term in (1) will be positive as their is a positive distance between it and ship 2. so in expanding out we will have the sum of negative numbers...is this correct?