Thomas Calculus 13th [Solutions]

920 Chapter 12 Vectors and the Geometry of Space
71.
2 2 2
x y z 72.
2 2 2
x z y 73.
2 2 2
x y z
4
74.
2 2 2
4y z 4x 4
75.
2 2 2
y x z 1
76.
2 2 2
z x y
1
CHAPTER 12 ADDITIONAL AND ADVANCED EXERCISES
1. Information from ship A indicates the submarine is now on the line L 1
1: x 4 2 t, y 3 t, z t ; information
3
from ship B indicates the submarine is now on the line L2 : x 18 s , y 5 6 s , z s . The current position of
the sub is 6, 3, 1 and occurs when the lines intersect at t 1 and s 1
3
3 . The straight line path of the
submarine contains both point P 2, 1, 1 and Q 6, 3, 1 ; the line representing this path is
3
3
L: x 2 4 t, y 1 4 t, z 1 . The submarine traveled the distance between P and Q in 4 minutes a
3
speed of | PQ | 32 2 thousand ft/min. In 20 minutes the submarine will move 20 2 thousand ft from Q
4 4
2 2 2 2 2 2
along the line L 20 2 2 4t 6 1 4t 3 0 800 16( t 1) 16( t 1) 32( t 1)
2
( t 1) 800 25 t 6 the submarine will be located at 26,23, 1 in 20 minutes.
32
3
2. H 2 stops its flight when 6 110t 446 t 4 hours. After 6 hours, H 1 is at P (246,57,9) while H 2 is at
2 2 2
(446,13,0). The distance between P and Q is (246 446) (57 13) (9 0) 204.98 miles. At 150
mph, it would take about 1.37 hours for H 1 to reach H 2 .
3. Torque PQ F 15ft-lb = PQ | F|sin 3 ft | F| | F|
20 lb
2 4
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