How Do You Calculate the Distance Between Two Moving Ships Using Vectors?

[turnstile]

Two ships P and Q are traveling at night with constant velocities. At midnight, P is at the point with position vector (20i + 10j) km relative to a fixed origin O. At the same time, Q is at the point with position vector (14i – 6j) km. Three hours later, P is at the point with position vector (29i + 34j) km. The ship Q travels with velocity 12j km h–1. At time t hours after midnight, the position vectors of P and Q are p km and q km respectively. Find
(a) the velocity of P, in terms of i and j,

(b) expressions for p and q, in terms of t, i and j.

At time t hours after midnight, the distance between P and Q is d km.
(c) By finding an expression for PQ, show that
d^2 = 25t^2 – 92t + 29^2.
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Hi... another vectors question...
i get the answers to part a and and b... however, for C i don't really know how to do this one... maybe I am lacking the principles to this question. ... If anyone could walk me through part C.. it would really help...
Thanks :)

PS. Do you know of any good internet source that has extensive tutorials on vectors?

 

[Hootenanny]

How'd you calculate the distance between two points on a graph? You should apply the same rule here.

~H

 

[turnstile]

(y2 -y1) ÷ (x2 -x1)?

 

[Hootenanny]

Using pythag;

$$d = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}$$

~H