Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point (x, y, z) on the line x = 6 + t, y = 8 t, z = 3 + t. Also, at time t, the second insect is at the point (x, y, z) on the line x = 1 + t, y = 2 + t, z = 2t. Assume that distances are given in inches.

(a) Find the distance between the two insects at time t = 0.

(b) Use a graphing utility to graph the distance between the insects from t = 0 to t = 10.

(c) Using the graph from part (b), what can you conclude about the distance between the insects?

(d) How close to each other do the insects get?