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Geometric Vectors

Page 490 Check for Understanding

1.Sample answer:

Draw a

u . Then draw b u so that its initial point (tip) is on the terminal point (tail) of a u . Draw a dashed line from the initial point of a u to the terminal point of b u . The dashed line is the resultant.

2.Sample answer: A vector has magnitude and

direction. A line segment has only length. A vector can be represented by a directed line segment.

3.Sample answer: the velocities of an airplane and a

wind current

4.No, they are opposites.

5-11.Answers may vary slightly.

5.1.2 cm, 120°6.2.9 cm, 55°7.1.4 cm, 20°

8. 9. 10. 8-1

245Chapter 8

Chapter 8 Vectors and Parametric Equations?a

a ? b?? b x ? y

3.5 cm??

x y 70
x ? y2.6 cm x ?y 210

12.9 cm

z 4y 51

3.5 cm, 70°

2.6 cm, 210°

12.9 cm, 51°11.

2.9 cm, 12°

12.h?2.9 cos 55°v?2.9 sin 55°

h?1.66 cmv?2.38 cm 13a.

13b.Use the Pythagorean Theorem.

c 2 ?a 2 ?b2 c 2 ?(100) 2 ?(5) 2 c 2 ?10,025 c??10,02 ?5 or about 100.12 m/s

Pages 491-492 Exercises

14.2.6 cm, 128°15.1.4 cm, 45°

16.2.1 cm, 14°17.3.0 cm, 340°

18-30.Answers may vary slightly.

18.

3 cm, 101°

19.

3.4 cm, 25°

20.

3.8 cm, 359°?x

13

2.9 cm

2z ?x 13 2z 12

51003 cmr

? s r s 101
? t?? s? t? 25

3.8 cms

? u?? su 359
21.

5.5 cm, 324°

22.

3.9 cm, 155°

23.

5.2 cm, 128°

24.

4.2 cm, 45°

25.

8.2 cm, 322°26.

3.5 cm, 22°

27.

5.4 cm, 133°

28.

5.5 cm, 358°

29.Draw to scale:

3.4 cm, 301°

30.Draw to scale:

11.7 cm, 357°

31.h??2.6 cos 128°?v??2.6 sin 128°?

h?1.60 cmv?2.05 cm

32.h??1.4 cos 45°?v??1.4 sin 45°?

h?0.99 cmv?0.99 cm

33.h??2.1 cos 14°?v??2.1 sin 14°?

h?2.04 cmv?0.51 cm

Chapter 8

246

5.5 cm

u ? ru? ?r? 324

3.9 cmr

? t? r? t?? 155

5.2 cm

r2r 128

4.2 cm3s

s 45

8.2 cm

3u ? 2s?? ?2s?

3u?322

3.5 cm

r ? t ? u??? r? t? u? 22

5.4 cmr

? s ? u r? s?u?? 133

5.5 cm

2s ? u ? r 12 2su? ? r 12 358

3.4 cm

r ? 2t ? s ? 3u?2t 3u? ?s? r? 301

11.7 cm

3t ? 2u 2u3t 357

34.h??3.0 cos 340°?v??3.0 sin 340°?

h?2.82 cmv?1.03 cm 35.c
2 ?a 2 ?b 2 c 2 ?(29.2) 2 ?(35.2) 2 c 2 ?2091.68 c??2091. ?68?or about 45.73 m

36.The difference of the vectors; sample answer: The

other diagonal would be the sum of one of the vectors and the opposite of the other vector, so it would be the difference.

37.Yes; sample answer:

38.

61 N, 23° north of east

39.Sometimes;

40a.v?1.5 sin 52°h?1.5 cos 52°

v?1.18 Nh?0.92 N

40b.h?1.5 cos 78°v?1.5 sin 78°

h?0.31 Nv?1.47 N41.h?47 cos 40°v?47 sin 40° h?36 mphv?30 mph

42.It is true when k?1 or when a

u is the zero vector. 43.c
2 ?a 2 ?b 2 c 2 ?(50) 2 ?(50) 2 c??5000?or about 71 lb 44.
a u ?b u ?24 equilateral triangle a u ?b u ?24 lb

45.The origin is not in the interior of the acute angle.

d 1 ??d 2 d 1 ??x 1? 2 y (?2 1) 2 or x? ??y? 2 2 d 2 y 0 2 ?5 1 2 or y?5 x? ??y? 2 2 ??(y?5) x?y?2 ??2 ?(y?5) x?y?2 ??2 ?y?5?2? x?y?2 ??2?y?5?2??0 x?(1 ??2 ?)y?2 ?5?2??0

46.csc vcos vtan v?

si1 nv ?cos v? cs oin sv v s si in nv v c co os sv v ?1 47.
4 ??nwhere nis an integer 48.
2 5 2? ?scl? 2 by [?3, 3] scl?1 x??, 3 2? for 0 ?x?2?

49.tan 18°29??

0.5 5b b?

0.5 tan5

18°29?

b?29.9 cm sin 18°29?? h5 h? sin 15

8°29?

h?15.8 cm

247Chapter 8

s ?s r ?r s ? rr ? s

6.160 N35 N

40 N
23
a?a ? b? ? 5 ? 5 b ?a? ? ?b? ? 2.3 ? 2.7?? a?a ? b? ? 1.5 ? 5 b a ? b?? ?a? ? ?b? ? 2.3 ? 2.7?? ab?? 60
60
60
60
60
60

2.4 cm

50.v
o ?volume of original box v n ?volume of new box v o o ?w o ?h o ?(w?1) ?w?2w ?(w?1)2w 2 ?2w 3 ?2w 2 v n n ?w n ?h n ?(w?2) ?(w?1) ?(2w?2) ?(w 2 ?3w?2)(2w?2) ?2w 3 ?8w 2 ?10w?4 2w 3 ?8w 2 ?10w?4 ?160 w o ?3 o ?2w ?2 ?3 or 6 h o ?w?1quotesdbs_dbs8.pdfusesText_14