Thread: Parametric Equations Help!

Two round pieces of rock are moving through space. The first rock has a diameter 0.3m and traveling on a line given by the parametric equation:

x(t) = 2+t, y(t) = -1 - t, z(t) = t

The second rock has a diameter of 0.1m and traveling on the line with parametric equation:

x(s) = 3 - s, y(s) = 1, z(s) = 1 + s

Calculate distance between the two lines and use this distance to prove that both rocks will not collide.

The distance is given by , now you'll get a function for the distance in terms of the time. Now show this function will never value (0.3+0.1), so the rocks don't collide.