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 x6+ty=8-tz 3+ t. Also, at time t, the second insect is at the point (x, y, z) on the line x=1+by=6+tz = 6t. Assume that distances are given in inches. (a) Find the distance between the two insects at time t = 0. (Round your answer to two decimal places.) 6.16 (6) Use a graphing utility to graph the distance between the insects from t = 0 tot = 6. 20 20 y Y 10 0 -10 -20 10 -10 -20- 1 2 3 X 4 6 y 10 Ⓡ 0 -10- O -20- y 10 0 -10 -20 (c) Using the graph from part (b), what can you conclude about the distance between the insects? Ⓒ The distance remains positive. O. The distance reaches zero. O The distance becomes negative. (d) How close to each other do the insects get? (Round your answer to two decimal places.) 5 in 1 2 3 X 4 5

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