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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 +t₁y = 6 + t, z = 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
(b) Use a graphing utility to graph the distance between the insects from t = 0 to t = 6.
20-
20
O
O
y
y
10
0
-10-
-20-
20
10
0
-10-
-20-
3
O The distance reaches zero.
O The distance becomes negative.
4
5
6
y
10
0
-10
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.
(d) How close to each other do the insects get? (Round your answer to two decimal places.)
5
in
1
3
3
X
4
4
5
5
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