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. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Linear algebra

    Let L be the line passing through the point P(−2, −2, 2) with direction vector d=[1, −2, 3]T. Find the shortest distance d from the point P0(−4, −4, −5) to L, and the point Q on L that is closest to P0. Use the square

  2. linear algebra

    Let L1 be the line passing through the point P1=(9, 0, 0) with direction vector →d1=[3, 2, −2]T, and let L2 be the line passing through the point P2=(−10, 8, 4) with direction vector →d2=[3, 0, 2]T. Find the shortest

  3. Calculus and vectors

    Vector AB is a vector whose tail is at (-4,2) and whose head is at (-1,3). Calculate the magnitude of vector AB Determine the coordinates of point D on vector CD, if C (-6,0) and vector CD= vector AB. Please I need some help. Is

  4. Math

    A vector t has initial point (-5,-2) and terminal point (-3,4). Write t in the form t=ai+bj.

  1. gen. physics II

    Two charges, +Q and ‑Q, are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated. Which vector best represents the direction of the electric field at that point? a.

  2. Precalculus

    Suppose that termial point by t is the point (3/4, (square root 7)/4) on the unit circle. Find the terminal point determined by each of the following. a) pi - t b) -t c) pi + t d) 2pi + t

  3. Geometry

    If vector v has an initial point at (2, 3) and a terminal point at (6, 6) and vector w has an initial point at (3, 2) and a terminal point at (6, 6), are the two vectors equivalent? A) Yes, they have the same magnitude and same

  4. calculus

    State whether or not the following statements are true. Justify your reasoning.? a. Vector a • (Vector b + Vector c) = Vector a • Vector b + Vector a • Vector c b. Vector a × (Vector b + Vector c) = Vector a × Vector b +

  1. algebra

    Let L1 be the line passing through the point P1=(4, 5, −5) with direction vector →d1=[0, −1, 1]T, and let L2 be the line passing through the point P2=(13, 0, 0) with direction vector →d2=[4, −1, 3]T. Find the shortest

  2. math

    Previously you found that a 15-degree counterclockwise rotation centered at(2,1)sends the point(4,6)to another point (x, y) ≈ (2.638, 6.347). The diagram on the right shows the vector v in the same direction as vector [2,5],

  3. physics

    A flywheel with a diameter of 1 m is initially at rest. Its angular acceleration versus time is graphed in the figure. (a) What is the angular separation between the initial position of a fixed point on the rim of the flywheel and

  4. Trig

    Sketch a unit circle and label the terminal points corresponding to t= pi/4, 3pi/4, 5pi/4, 7pi/4. Include the coordinates of each point. I have 3 other problems like this and i have no clue how to do them. can someone help please?

You can view more similar questions or ask a new question.