Chapter 13.5, Problem 38E

Intersecting lines and colliding particles Consider the lines

r = $\langle 2+2t,8+t,10+3t\rangle$ and

R = $\langle 6+s,10-2s,16-s\rangle$

a. Determine whether the lines intersect (have a common point), and if so, find the coordinates of that point.

b. If r and R describe the paths of two particles, do the particles collide? Assume t ≥ 0 and s ≥ 0 measure time in seconds, and that motion starts at s = t = 0.