Chapter 11.5, Problem 59ES

Two bugs are walking along lines in 3-space. At time t bug 1 is at the point $\left(x,y,z\right)$ on the line $x=4-t,y=1+2t,z=2+t$ and at the same time t bug 2 is at the point $\left(x,y,z\right)$ on the line $x=t,y=1+t,z=1-1-2t$ Assume that distance is in centimeters and that time is in minutes.

(a) Find the distance between the bugs at time $t=0.$

(b) Use a graphing utility to graph the distance between the bugs as a function of time from $t=0\text{ to }t=5.$

(c) What does the graph tell you about the distance between the bugs?

(d) How close do the bugs get?