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April 16, 2014

Homework Help: geometry

Posted by Cam on Wednesday, December 7, 2011 at 7:13pm.

1. Initial point: (0, 0); Terminal point: (3, -4)

A Lesson 13
B Lesson 13
C Lesson 13
D Lesson 13
E Lesson 13
F Lesson 13

2. Initial point: (3, 5); Terminal point: (-2, -1)

A Lesson 13
B Lesson 13
C Lesson 13
D Lesson 13
E Lesson 13
F Lesson 13

In problems 3 and 4, let u = Lesson 13, v = Lesson 13, and w = Lesson 13. Find the component form of the vector.

3. 2u + 3w

A Lesson 13
B Lesson 13
C Lesson 13
D Lesson 13
E Lesson 13
F Lesson 13

4. -2u - 3v

A Lesson 13
B Lesson 13
C Lesson 13
D Lesson 13
E Lesson 13
F Lesson 13

5. Find a unit vector in the direction of v = Lesson 13. Write your answer as a linear combination of the standard unit vectors i and j. Round each component to the nearest hundredth, if necessary.

A 0.71i - 0.71j
B 0i - 0j
C 1.41i - 1.41j
D 1i - 1j
E 2.83i - 3.83j
F -1i - 1j


6. Find the component form of v if the direction angle is 55 and the magnitude is 14. (See diagram below.) Round each component to the nearest hundredth, if necessary.

A vLesson 13
B v Lesson 13
C v Lesson 13
D v Lesson 13
E v Lesson 13
F v Lesson 13


For problems 7 and 8, find the magnitude and direction angle of the given vector.

7. Lesson 13

A magnitude: 5; direction angle: 53.13
B magnitude: Lesson 13; direction angle: 53.13
C magnitude: Lesson 13; direction angle: 3.40
D magnitude: Lesson 13; direction angle: 0.80
E magnitude:5; direction angle: 3.40
F magnitude: 5; direction angle: 0.80

8. -3i - 5j

A magnitude: Lesson 13; direction angle: 120.96
B magnitude: Lesson 13; direction angle: 239.04
C magnitude: Lesson 13; direction angle: 59.04
D magnitude: 34; direction angle: 84.94
E magnitude: 34; direction angle: 95.06
F magnitude: 34; direction angle: 275.06

For problems 9 - 11, find the dot product if u = Lesson 13, v = Lesson 13, and w = Lesson 13.

9. Lesson 13

A 2
B 8
C -10
D 10
E 4
F -3


10. Lesson 13

A -11
B 0
C 1
D -17
E 11
F -1

11. Lesson 13

A 37
B -37
C -33
D -29
E 29
F 9

For problems 12 and 13, using the theorem given in this lesson, find the angle between the given vectors.

12. Lesson 13 and Lesson 13

A 88.3
B 55.5
C 11
D 74.92
E 1.7
F 62.4

13. Lesson 13 and Lesson 13

A 120
B 60
C 315
D 225
E 135
F 45

14. An airplane is flying on a bearing of 335 at 530 miles per hour. Find the component form of the velocity of the airplane.

A v Lesson 13
B v Lesson 13
C v Lesson 13
D v Lesson 13
E v Lesson 13
F v Lesson 13

15. An airplane is flying on a bearing of 170 at 460 miles per hour. Find the component form of the velocity of the airplane.

A v Lesson 13
B v Lesson 13
C v Lesson 13
D v Lesson 13
E v Lesson 13
F v Lesson 13

16. Now, assume that the airplane from problem 12 is flying in a wind that is blowing with the bearing 200 at 80 miles per hour. Find the actual ground speed of the airplane.

A 530.79 miles per hour
B 52.52 miles per hour
C 528.19 miles per hour
D 24.09 miles per hour
E 23.08 miles per hour
F 453.01 miles per hour

17. Use the information from problem 13 to find the actual direction (angle) of the airplane. (This is the angle from the horizontal x-axis, not the bearing.)

A 174.32
B -75.18
C 250
D -80
E 80
F 84.32

18. A basketball is shot at a 70 angle with the horizontal with an initial velocity of 10 meters per second. Find the component form of the initial velocity.

A v Lesson 13
B v Lesson 13
C v Lesson 13
D v Lesson 13
E vLesson 13
F v Lesson 13

19. A force of 50 pounds acts on an object at an angle of 45. A second force of 75 pounds acts on the object at an angle of -30. Find the direction and magnitude of the resultant force.

A magnitude: 2.14 lbs; direction: -2.14
B magnitude: 125 lbs; direction: -30
C magnitude: 125 lbs; direction: -1.22
D magnitude: 100.33 lbs; direction: 15
E magnitude: 100.33 lbs; direction: -1.22
F magnitude: 2.14 lbs; direction: 15


20. Juana and Diego Gonzales, ages six and four respectively, own a strong and stubborn puppy named Corporal. It is so hard to take Corporal for a walk that they devise a scheme to use two leashes. If Juana pulls with a force of 23 lbs at an angle of 18° and Diego pulls with a force of 27 lbs at an angle of -15, how hard is Corporal pulling if the puppy holds the children at a standstill?

A 50 lbs
B 4 lbs
C 3 lbs
D 47.95 lbs
E 33 lbs
F 7 lbs

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