1. Precalculus
Chapter 8 Study Guide Solutions
Vocabulary:
1. Resultant 4. Cross 7. Standard
2. Unit 5. Inner 8. Components
3. Magnitude 6. Parallel
1. 142°, 2.1 cm 2. 36°, 1.6 cm 3. 298°, 3.4 cm
! !
v = !5,12 v = 3, 4
7. ! 8. !
v = 13 v =5
! !
v = 0, 0, 0 v = !4, !6, 8
9. ! 10. !
v =0 v = 2 29
! ! !28 !34 !
11. a = !22, 29 12. a= , 13. a = 44, 32
3 3
! !15 23 ! ! 50 71
14. u = 12, , 15. u = !5, !24, 8 16. u= , !13,
2 2 3 3
!
17. 7. !5i + 12 ˆ
ˆ j 8. 3i + 4 ˆ
ˆ j 9. 0
ˆ !28 ˆ 34 ˆ
10. !4 i ! 6 ˆ + 8 k
ˆ j 11. !22i + 29 ˆ
ˆ j 12. i! j
3 3
13. 44 i + 32 ˆ
ˆ j
18. 0; yes 19. -21; no 20.
32; no
21. 6; no 22. 0; yes 23.
9; no
24. j ˆ
!34 i ! 2 ˆ + 22 k
ˆ 25. ˆ
10 k ˆ
26. j ˆ
8i + 8 ˆ + 16 k
27. ˆ j ˆ
More than one possible answer. Ex: !5, 0, !4 " 4, !5, !3 = !20i ! 31 ˆ + 25 k
30. x ! 5, y ! 7 = t 2, 0 31. x + 1, y ! 4 = t 6, !10
x = 2t + 5 x = 6t ! 1
y=7 y = !10t + 4
32. x ! 1, y ! 5 = t !7, 2 33. x=t
x = !7t + 1 3 7
y= t+
y = 2t + 5 4 4
x=t x=t
34. 35.
y = !9t ! 1 y = 4t ! 2
1 1 23 5 17
36. y = ! x +1 37. y= x+ 38. y= x!
2 4 4 2 2

2. 40. a) Pallas: x = !7 + 2t, y = !6 + 2t, z = !1 + t
Ceres: x = !1 + t, y = 4 ! t, z = !1 + 2t
b) yes, (1, 2, 3)
1 1
41. x = ! + t y = 1 + 4t z = 1 ! 9t
3 3
42. horizontal: 28.86 ft/s, vertical: 16.00 ft/s
43. horizontal: 39.61 m, vertical: 2.43 m
" 3 3 3 3 !4 !4 !4 !4 %
$ '
44. a) $ !2 !2 4 4 4 4 !2 !2 '
$ 2 !1 !1 2 2 !1 !1 2 '
# &
" 5 5 5 5 !2 !2 !2 !2 %
$ '
b)
$ !2 !2 4 4 4 4 !2 !2 '
$
# 5 2 2 5 5 2 2 5 ' &
" 3 3 3 3 !4 !4 !4 !4 %
$ '
c)
$ 2 2 !4 !4 !4 !4 2 2 '
$
# 2 !1 !1 2 2 !1 !1 2 '&