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,-1,1)=

Algebra & Trigonometry with Analytic Geometry
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Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 84E
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Calculus 3 Do only 5 and 7 step by step please
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,)
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, 1, 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 is pointing
due north and travelling at a speed of 4 knots
relative to the water. There is a current flowing
due east at 1 knot. (The units on the chart are
nautical miles; 1 knot = 1 nautical mile per
hour.)
(a) If there were no current, what vector u
would represent the velocity of the ship rela-
tive to the sea bottom?
Copyright 1985 Spring
Transcribed Image Text: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,) 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, 1, 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 is pointing due north and travelling at a speed of 4 knots relative to the water. There is a current flowing due east at 1 knot. (The units on the chart are nautical miles; 1 knot = 1 nautical mile per hour.) (a) If there were no current, what vector u would represent the velocity of the ship rela- tive to the sea bottom? Copyright 1985 Spring
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