# geometry

In problems 1 and 2, the initial point and the terminal point of a vector are given. Write the vector in component form.

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

1. 👍
2. 👎
3. 👁
1. 1. (0,0), (3,-4).
X = x2 - x1 = 3-0 = 3,
Y = y2 - y1 = -4 - 0 = -4,

Component Form = (X,Y) = (3,-4).

2. (3,5), (-2,-1).
X = = x2 - x1 = -2 -3 = -5.
Y = y2 - y1 = -1 - 5 = -6.

Component Form = (X,Y) = (-5,-6).

1. 👍
2. 👎

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