5. (6,0, 5) + (5,0,6)=

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 30E
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Exercises for Section 13.2
Plot the points in Exercises 1-4.
1. (1,0,0)
3. (3,-1,5)
2. (0,2,4)
4. (2,-1,1)
Complete the computations in Exercises 5-8.
5. (6,0, 5) + (5,0, 6) =
6. (0,0,0) + (0,0,0) =
7. (1,3,5) + 4(-1, -3, -5) =
8. (2,0, 1)-8(3, — ½, 4) =
9. Sketch v, 2v, and -v, where v has components
(1,-1,-1).
10. Sketch v, 3v, and - v, where v has components
(2, -1, 1).
11. Let v have components (0, 1, 1) and w have com-
ponents (1, 1, 0). Find v + w and sketch.
12. Let v have components (2, -1, 1) and w have
components (1,-1,-1). Find v + w and sketch.
In Exercises 13-20, express the given vector in terms of
the standard basis.
13. The vector with components (-1, 2, 3).
14. The vector with components (0, 2, 2).
15. The vector with components (7,2, 3).
16. The vector with components (-1,2, 7).
17. The vector from (0, 1, 2) to (1, 1, 1).
18. The vector from (3, 0, 5) to (2, 7, 6).
19. The vector from (1, 0, 0) to (2, -1, 1).
20. The vector from (1,0,0) to (3,-2, 2).
21. A ship at position (1,0) on a nautical chart (with
north in the positive y direction) sights a rock at
position (2, 4). What is the vector joining the ship
to the rock? What angle does this vector make
with due north? This is called the bearing of the
rock from the ship.
22. Suppose that the ship in Exercise 21
due north and travelling at a speed
Page
relative to the water. There is a current nowing
Open
23. A
a
m
p
(a
24. TH
eas
spe
spe
vec
(a)
(b)
25. A f
(b
tal,
and
figu
26. Two
15 / 50
to a
A PL
a for
(a)
17
th
Transcribed Image Text:df earch Exercises for Section 13.2 Plot the points in Exercises 1-4. 1. (1,0,0) 3. (3,-1,5) 2. (0,2,4) 4. (2,-1,1) Complete the computations in Exercises 5-8. 5. (6,0, 5) + (5,0, 6) = 6. (0,0,0) + (0,0,0) = 7. (1,3,5) + 4(-1, -3, -5) = 8. (2,0, 1)-8(3, — ½, 4) = 9. Sketch v, 2v, and -v, where v has components (1,-1,-1). 10. Sketch v, 3v, and - v, where v has components (2, -1, 1). 11. Let v have components (0, 1, 1) and w have com- ponents (1, 1, 0). Find v + w and sketch. 12. Let v have components (2, -1, 1) and w have components (1,-1,-1). Find v + w and sketch. In Exercises 13-20, express the given vector in terms of the standard basis. 13. The vector with components (-1, 2, 3). 14. The vector with components (0, 2, 2). 15. The vector with components (7,2, 3). 16. The vector with components (-1,2, 7). 17. The vector from (0, 1, 2) to (1, 1, 1). 18. The vector from (3, 0, 5) to (2, 7, 6). 19. The vector from (1, 0, 0) to (2, -1, 1). 20. The vector from (1,0,0) to (3,-2, 2). 21. A ship at position (1,0) on a nautical chart (with north in the positive y direction) sights a rock at position (2, 4). What is the vector joining the ship to the rock? What angle does this vector make with due north? This is called the bearing of the rock from the ship. 22. Suppose that the ship in Exercise 21 due north and travelling at a speed Page relative to the water. There is a current nowing Open 23. A a m p (a 24. TH eas spe spe vec (a) (b) 25. A f (b tal, and figu 26. Two 15 / 50 to a A PL a for (a) 17 th
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