Consider the lines

r(t) = (2 + 2t, 8 + t, 10 + 3t) and
R(s) = (6 + s, 10 - 2s, 16 - s).

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 that t ≥ 0 and s ≥ 0 measure time in seconds, and that motion starts at s = t = 0.