Distance Between Two Particles at Time t = pi

[mrkb80]

Homework Statement

The position of a particle at time t is given by r(t) = 3(t² - sin t)i +
tj - (cos t)k , and the position of another particle is R(t) = t²i + (t³ +
t)j+(sin t)k . At time t = pi, what is the rate of change of the distance
between the two particles? Are they getting closer to one another, or
are they getting farther apart?

Homework Equations

The Attempt at a Solution

I'm actually not sure how to attempt this problem. I think that if the rate of change is positive they are getting farther apart and if it is negative they are getting closer, but I'm not sure.

 

[hotvette]

The first thing you need to do is write an expression for the distance between the two particles. Think pythagorean theorem.

 

[mrkb80]

I'm not sure I understand. Do I subtract the square of the i,j,k components from each other to get d^2 and then take the directional derivative?