Exam Prep Chapter.3 Vectors 11th Edition - Physics Extended 11e | Test Bank by Halliday by David Halliday. DOCX document preview.
Chapter: Chapter 3
Learning Objectives
LO 3.1.0 Solve problems related to vectors and their components
LO 3.1.1 Add vectors by drawing them in head-to-tail arrangements, applying the commutative and associative laws.
LO 3.1.2 Subtract a vector from a second one.
LO 3.1.3 Calculate the components of a vector on a given coordinate system, showing them in a drawing.
LO 3.1.4 Given the components of a vector, draw the vector and determine its magnitude and orientation.
LO 3.1.5 Convert angle measures between degrees and radians.
LO 3.2.0 Solve problems related to unit vectors and adding vectors by components
LO 3.2.1 Convert a vector between magnitude-angle and unit-vector notations.
LO 3.2.2 Add and subtract vectors in magnitude-angle notation and in unit-vector notation.
LO 3.2.3 Identify that, for a given vector, rotating the coordinate system about the origin can change the vector’s components but not the vector itself.
LO 3.3.0 Solve problems related to multiplying vectors
LO 3.3.1 Multiply vectors by scalars.
LO 3.3.2 Identify that multiplying a vector by a scalar gives a vector, taking the dot (or scalar) product of two vectors gives a scalar, and taking the cross (or vector) product gives a new vector that is perpendicular to the original two.
LO 3.3.3 Find the dot product of two vectors in magnitude-angle notation and in unit-vector notation.
LO 3.3.4 Find the angle between two vectors by taking their dot product in both magnitude-angle notation and unit-vector notation.
LO 3.3.5 Given two vectors, use a dot product to find how much of one vector lies along the other vector.
LO 3.3.6 Find the cross product of two vectors in magnitude-angle and unit-vector notations.
LO 3.3.7 Use the right-hand rule to find the direction of the vector that results from a cross product.
LO 3.3.8 In nested products, where one product is buried inside another, follow the normal algebra procedure by starting with the innermost product and working outward.
Multiple Choice
1. We say that the displacement of a particle is a vector quantity. Our best justification for this assertion is:
A) displacement can be specified by a magnitude and a direction
B) operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments
C) a displacement is obviously not a scalar
D) displacement can be specified by three numbers
E) displacement is associated with motion
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.0
2. A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is:
A) 0
B) 1
C) 3
D) 5
E) 7
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.1
3. A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum can be:
A) 0
B) 3
C) 12
D) 47
E) 50
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.1
4. A vector of magnitude 6 and another vector have a resultant of magnitude 12. The vector :
A) must have a magnitude of at least 6 but no more than 18
B) may have a magnitude of 20
C) cannot have a magnitude greater than 12
D) must be perpendicular to
E) must be perpendicular to the resultant vector
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.1
5. If , then:
A) and must be parallel and in the same direction
B) and must be parallel and in opposite directions
C) it must be true that either or is zero
D) the angle between and must be 60
E) none of the above is true
Difficulty: Medium
Section: 3-1
Learning Objective 3.1.1
6. If and neither nor vanish, then:
A) and are parallel and in the same direction
B) and are parallel and in opposite directions
C) the angle between and is 45
D) the angle between and is 60
E) is perpendicular to
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.1
7. The vector is:
A) greater than in magnitude
B) less than in magnitude
C) in the same direction as
D) in the direction opposite to
E) perpendicular to
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.0
8. The vectors , , and are related by . Which diagram below illustrates this relationship?
A) I.
B) II.
C) III.
D) IV.
E) None of these
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.2
9. The vector in the diagram is equal to:
A)
B)
C)
D)
E)
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.2
10. If and neither nor vanish, then:
A) and are parallel and in the same direction
B) and are parallel and in opposite directions
C) the angle between and is 45
D) the angle between and is 60
E) is perpendicular to
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.2
11. Four vectors all have the same magnitude. The angle between adjacent vectors is 45 as shown. The correct vector equation is:
A)
B)
C)
D)
E)
Difficulty: Hard
Section: 3-1
Learning Objective 3.1.2
12. Vectors and lie in the xy plane. We can deduce that if:
A) Ax2 + Ay2 = Bx2 + By2
B) Ax + Ay = Bx + By
C) Ax = Bx and Ay = By
D) Ay /Ax = By /Bx
E) Ax = Ay and Bx = By
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.0
13. One radian is approximately
A) 10°
B) 33°
C) 57°
D) 90°
E) 180°
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.5
14. 30° is
A) π/10 radians
B) π/6 radians
C) 1 radian
D) π/2 radians
E) π radians
Difficulty: Easy
Section: 3-1
Learning Objective 3.1.5
15. A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x axis and negative y axis and makes an angle of 30 with the x axis. Its y component is:
A)
B)
C) 6
D) –6
E) 12
Difficulty: Easy
Section: 3-1
Learning Objective 3.2.1
16. If the x component of a vector , in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x axis is:
A)
B) 1/2
C)
D) 3/2
E) 3
Difficulty: Medium
Section: 3-1
Learning Objective 3.2.1
17. A vector has a component of 10 m in the +x direction, a component of 10 m in the +y direction, and a component of 5 m in the +z direction. The magnitude of this vector is:
A) 0 m
B) 15 m
C) 20 m
D) 25 m
E) 225 m
Difficulty: Easy
Section: 3-1
Learning Objective 3.2.1
18. Let . The magnitude of is:
A) 5.00
B) 5.57
C) 7.00
D) 7.42
E) 8.54
Difficulty: Easy
Section: 3-2
Learning Objective 3.2.1
19. A vector in the xy plane has a magnitude of 25 and an x component of 12. The angle it makes with the positive x axis is:
A) 26
B) 29
C) 61
D) 64
E) 241
Difficulty: Easy
Section: 3-1
Learning Objective 3.2.1
20. The angle between = (25 m) + (45 m) and the positive x axis is:
A) 29
B) 61
C) 151
D) 209
E) 241
Difficulty: Easy
Section: 3-2
Learning Objective 3.2.1
21. The angle between = −(25 m) + (45 m) and the positive x axis is:
A) 29
B) 61
C) 119
D) 151
E) 209
Difficulty: Medium
Section: 3-2
Learning Objective 3.2.1
22. Let = (2 m) + (6 m) – (3 m) and = (4 m) + (2 m) + (1 m). The vector sum is:
A) (6 m) + (8 m) – (2 m)
B) (−2 m) + (4 m) – (4 m)
C) (2 m) − (4 m) + (4 m)
D) (8 m) + (12 m) – (3 m)
E) none of these
Difficulty: Easy
Section: 3-2
Learning Objective 3.2.2
23. Let = (2 m) + (6 m) – (3 m) and = (4 m) + (2 m) + (1 m). The vector difference is:
A) (6 m) + (8 m) – (2 m)
B) (−2 m) + (4 m) – (4 m)
C) (2 m) − (4 m) + (4 m)
D) (8 m) + (12 m) – (3 m)
E) none of these
Difficulty: Easy
Section: 3-2
Learning Objective 3.2.2
24. If = (2 m) − (3 m) and = (1 m) − (2 m), then =
A) (1 m)
B) (−1 m)
C) (4 m) − (7 m)
D) (4 m) + (1 m)
E) (−4 m) + (7 m)
Difficulty: Easy
Section: 3-2
Learning Objective 3.2.2
25. In the diagram, has magnitude 12 m and has magnitude 8 m. The x component of is about:
A) 1.5 m
B) 4.5 m
C) 12 m
D) 15 m
E) 20 m
Difficulty: Medium
Section: 3-2
Learning Objective 3.2.2
26. A certain vector in the xy plane has an x component of 4 m and a y component of 10 m. It is then rotated in the xy plane so its x component is doubled. Its new y component is about:
A) 20 m
B) 7.2 m
C) 5.0 m
D) 4.5 m
E) 2.2 m
Difficulty: Medium
Section: 3-2
Learning Objective 3.2.3
27. If = (6 m) – (8 m) then has magnitude:
A) -8 m
B) 8 m
C) 10 m
D) 40 m
E) 56 m
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.1
28. Which of the following is correct?
A) Multiplying a vector by a scalar gives a scalar result.
B) Multiplying a vector by a vector always gives a vector result.
C) Multiplying a vector by a vector never gives a scalar result.
D) The only type of vector multiplication that gives a scalar result is the dot product.
E) The only type of vector multiplication that gives a vector result is the cross product.
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.2
29. Vectors and each have magnitude L. When drawn with their tails at the same point, the angle between them is 30. The value of is:
A) 0
B) L2
C)
D) 2L2
E) none of these
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.3
30. Let = (2 m) + (6 m) – (3 m) and = (4 m) + (2 m) + (1 m). Then equals:
A) (8 m) + (12 m) – (3 m)
B) (12 m) − (14 m) – (20 m)
C) 23
D) 17
E) none of these
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.3
31. Two vectors lie with their tails at the same point. When the angle between them is increased by 20 their scalar product has the same magnitude but changes from positive to negative. The original angle between them was:
A) 0°
B) 60
C) 70
D) 80
E) 90
Difficulty: Hard
Section: 3-3
Learning Objective 3.3.3
32. Let = (1 m) + (2 m) + (2 m) and = (3 m) + (4 m). The angle between these two vectors is given by:
A) cos–1(14/15)
B) cos–1(11/225)
C) cos–1(104/225)
D) cos–1(11/15)
E) cannot be found since and do not lie in the same plane
Difficulty: Medium
Section: 3-3
Learning Objective 3.3.4
33. Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65. The component of the longer vector along the line of the shorter is:
A) 0
B) 4.2
C) 6.3
D) 9.1
E) 14
Difficulty: Medium
Section: 3-3
Learning Objective 3.3.5
34. If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:
A) the scalar product of the vectors must be negative
B) the scalar product of the vectors must be positive
C) the vectors must be parallel and in opposite directions
D) the vectors must be parallel and in the same direction
E) none of the above
Difficulty: Medium
Section: 3-3
Learning Objective 3.3.0
35. If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then:
A) the scalar product of the vectors must be negative
B) the scalar product of the vectors must be positive
C) the vectors must be parallel and in opposite directions
D) the vectors must be parallel and in the same direction
E) none of the above
Difficulty: Medium
Section: 3-3
Learning Objective 3.3.0
36. Vectors and each have magnitude L. When drawn with their tails at the same point, the angle between them is 30. The magnitude of is:
A) L2/2
B) L2
C)
D) 2L2
E) none of these
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.6
37. Two vectors lie with their tails at the same point. When the angle between them is increased by 20 the magnitude of their vector product doubles. The original angle between them was about:
A) 0°
B) 18
C) 25
D) 45
E) 90
Difficulty: Hard
Section: 3-3
Learning Objective 3.3.0
38. The two vectors (3 m) − (7 m) and (2 m) + (3 m) − (2 m) define a plane (it is the plane of the triangle with both tails at one vertex and each head at one of the other vertices). Which of the following vectors is perpendicular to the plane?
A) (14 m) + (6 m) + (23 m)
B) (−14 m) + (6 m) + (23 m)
C) (14 m) − (6 m) + (23 m)
D) (14 m) + (6 m) − (23 m)
E) (14 m) + (6 m)
Difficulty: Medium
Section: 3-3
Learning Objective 3.3.6
39. Let and 90, where is the angle between and when they are drawn with their tails at the same point. Which of the following is NOT true?
A)
B)
C)
D)
E)
Difficulty: Medium
Section: 3-3
Learning Objective 3.3.6
40. The value of is:
A) 0
B) +1
C) –1
D) 3
E)
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.7
41. The value of is:
A) 0
B) +1
C) –1
D) 3
E)
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.7
42. The value of is:
A) 0
B) +1
C) –1
D) 3
E)
Difficulty: Easy
Section: 3-3
Learning Objective 3.3.8
43. The result of is:
A) 0
B) +1
C)
D)
E)
Difficulty: Medium
Section: 3-3
Learning Objective 3.3.8