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
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
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
4. If |???? + �⃗⃗�|
2
= ????2 + ????2, 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
5. 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 �⃗⃗�
6. 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 ????
7. The vectors �⃗�, �⃗⃗�, and ???? are related by ???? = �⃗� − �⃗⃗�. Which diagram below illustrates this relationship?
A) I.
B) II.
C) III.
D) IV.
E) None of these
8. The vector ????3⃗⃗ ⃗⃗ in the diagram is equal to:
A) ????1⃗⃗ ⃗⃗ − ????2⃗⃗ ⃗⃗
B) ????1⃗⃗ ⃗⃗ + ????2⃗⃗ ⃗⃗
C) ????2⃗⃗ ⃗⃗ − ????1⃗⃗ ⃗⃗
D) ????1⃗⃗ ⃗⃗ cos ????
9. Vectors ???? and �⃗⃗� lie in the xy plane. We can deduce that ???? = �⃗⃗� if:
A) Ax
2 + Ay
2 = Bx
2 + By
2
B) Ax + Ay = Bx + By
C) Ax = Bx and Ay = By
D) Ay /Ax = By /Bx
E) Ax = Ay and Bx = By
10. Two radians is approximately
A) 105°
B) 115°
C) 570°
D) 90°
E) 180°
11. 30° is
A) π/10 radians
B) π/6 radians
C) 1 radian
D) π/2 radians
E) π radians
12. 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) 6√3
B) −6√3
C) 6
D) –6
E) 12
13. 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
14. Let �⃗⃗� = 2.00????̂ + 6.00????̂ − 3.00�̂�. The magnitude of �⃗⃗� is:
A) 5.00
B) 5.57
C) 7.00
D) 7.42
E) 8.54
15. 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
16. The angle between ???? = (24.0 m)????̂ + (32.0 m)????̂ and the positive x axis is:
A) 29.2
B) 36.9
C) 53.1
D) 61.1
E) 127
17. The angle between ???? = −(24.0 m)????̂ + (32.0m)????̂ and the positive x axis is:
A) 29.2
B) 36.9
C) 53.1
D) 61.1
E) 127
18. 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
19. 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
20. If ???? = (2 m)????̂ − (3 m)????̂ and �⃗⃗� = (1 m)????̂ − (2 m)????̂, then ???? − 2�⃗⃗� =
A) (1 m)????̂
B) (−1 m)????̂
C) (4 m)????̂ − (7 m)????̂
D) (4 m)????̂ + (1 m)????̂
E) (−4 m)????̂ + (7 m)????̂
21. 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.
22. 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
23. 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
24. 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
25. The value of ????̂ ∙ (????̂ × �̂�) is:
A) 0
B) +1
C) –1
D) 3
E) √3
26. The value of �̂� ∙ (�̂� × ????̂) is:
A) 0
B) +1
C) –1
D) 3
E) √3
27. The value of (????̂ × �̂�) ∙ (�̂� × ????̂) is:
A) 0
B) +1
C) –1
D) 3
E) √3
28. The result of (????̂ × �̂�) × (�̂� × ????̂) is:
A) 0
B) +1
C) ????̂
D) ????̂
E) �̂�
29. Which expression is false concerning the vectors shown in the sketch?
A) C = A + B
B) C + A = – B
C) A + B + C = 0
D) C < A + B
E) A 2 + B 2 = C 2
30. A student adds two displacement vectors with magnitudes of 6.0 m and 8.0 m, respectively.
Which one of the following could not be a possible choice for the resultant?
A) 2.3 m
B) 6.6 m
C) 10.0 m
D) 12.8 m
E) 14.8 m
