Halliday/Resnick/Walker
Fundamentals of Physics
Classroom Response System Questions
Chapter 3 Vectors
Interactive Lecture Questions
3.2.1. Which one of the following statements is true concerning scalar
quantities?
a) Scalar quantities must be represented by base units.
b) Scalar quantities have both magnitude and direction.
c) Scalar quantities can be added to vector quantities using rules of
trigonometry.
d) Scalar quantities can be added to other scalar quantities using rules
of trigonometry.
e) Scalar quantities can be added to other scalar quantities using rules
of ordinary addition.
3.2.1. Which one of the following statements is true concerning scalar
quantities?
a) Scalar quantities must be represented by base units.
b) Scalar quantities have both magnitude and direction.
c) Scalar quantities can be added to vector quantities using rules of
trigonometry.
d) Scalar quantities can be added to other scalar quantities using rules
of trigonometry.
e) Scalar quantities can be added to other scalar quantities using rules
of ordinary addition.
3.2.2. Which one of the following situations involves a vector?
a) The submarine followed the coastline for 35 kilometers.
b) The air temperature in Northern Minnesota dropped to 4 C.
c) The Hubble Telescope orbits 598 km above the surface of the earth.
d) The baseball flew into the dirt near home plate at 44 m/s.
e) The flock of Canadian Geese was spotted flying due south at 5 m/s.
3.2.2. Which one of the following situations involves a vector?
a) The submarine followed the coastline for 35 kilometers.
b) The air temperature in Northern Minnesota dropped to 4 C.
c) The Hubble Telescope orbits 598 km above the surface of the earth.
d) The baseball flew into the dirt near home plate at 44 m/s.
e) The flock of Canadian Geese was spotted flying due south at 5 m/s.
3.3.1. 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) A2 + B2 = C2
3.3.1. 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) A2 + B2 = C2
3.3.2. Three vectors A , B , and C add together to yield zero: A + B + C
= 0. The vectors A and C point in opposite directions and their
magnitudes are related by the expression: A = 2C. Which one of
the following conclusions is correct?
a) B and C point in the same direction, but C has twice the magnitude
of B.
b) B and C have equal magnitudes and point in opposite directions.
c) A and B point in the same direction, but A has twice the magnitude
of B.
d) A and B have equal magnitudes and point in opposite directions.
e) B and C have equal magnitudes and point in the same direction.
3.3.2. Three vectors A , B , and C add together to yield zero: A + B + C
= 0. The vectors A and C point in opposite directions and their
magnitudes are related by the expression: A = 2C. Which one of
the following conclusions is correct?
a) B and C point in the same direction, but C has twice the magnitude
of B.
b) B and C have equal magnitudes and point in opposite directions.
c) A and B point in the same direction, but A has twice the magnitude
of B.
d) A and B have equal magnitudes and point in opposite directions.
e) B and C have equal magnitudes and point in the same direction.
3.3.3. Two vectors a and b are added together to form a vector c . The
relationship between the magnitudes of the vectors is given by a +
b = c. Which one of the following statements concerning these
vectors is true?
a) a and b must point in the same direction.
b) a and b must be displacements.
c) a and b must be at right angles to each other.
d) a and b must point in opposite directions.
e) a and b must have equal lengths.
3.3.3. Two vectors a and b are added together to form a vector c . The
relationship between the magnitudes of the vectors is given by a +
b = c. Which one of the following statements concerning these
vectors is true?
a) a and b must point in the same direction.
b) a and b must be displacements.
c) a and b must be at right angles to each other.
d) a and b must point in opposite directions.
e) a and b must have equal lengths.
3.3.4. Two vectors a and b are added together to form a vector c . The
relationship between the magnitudes of the vectors is given by a2 +
b2 = c2. Which one of the following statements concerning these
vectors is true?
a) a and b must be parallel.
b) a and b could have any orientation relative to each other.
c) a and b must be at right angles to each other.
d) a and b must point in opposite directions.
e) a and b must have equal lengths.
3.3.4. Two vectors a and b are added together to form a vector c . The
relationship between the magnitudes of the vectors is given by a2 +
b2 = c2. Which one of the following statements concerning these
vectors is true?
a) a and b must be parallel.
b) a and b could have any orientation relative to each other.
c) a and b must be at right angles to each other.
d) a and b must point in opposite directions.
e) a and b must have equal lengths.
3.3.5. What is the minimum number of vectors with unequal
magnitudes whose vector sum can be zero?
a) 2
b) 3
c) 4
d) 5
e) 6
3.3.5. What is the minimum number of vectors with unequal
magnitudes whose vector sum can be zero?
a) 2
b) 3
c) 4
d) 5
e) 6
3.3.6. What is the minimum number of vectors with equal magnitudes
whose vector sum can be zero?
a) 2
b) 3
c) 4
d) 5
e) 6
3.3.6. What is the minimum number of vectors with equal magnitudes
whose vector sum can be zero?
a) 2
b) 3
c) 4
d) 5
e) 6
3.3.7. A physics student adds two displacement vectors with magnitudes of
8.0 km and 6.0 km. Which one of the following statements is true
concerning the magnitude of the resultant displacement?
a) The magnitude must be 14.0 km.
b) The magnitude must be 10.0 km.
c) The magnitude could be equal to zero kilometers, depending on
how the vectors are oriented.
d) The magnitude could have any value between 2.0 km and 14.0 km,
depending on how the vectors are oriented.
e) No conclusion can be reached without knowing the directions of the
vectors.
3.3.7. A physics student adds two displacement vectors with magnitudes of
8.0 km and 6.0 km. Which one of the following statements is true
concerning the magnitude of the resultant displacement?
a) The magnitude must be 14.0 km.
b) The magnitude must be 10.0 km.
c) The magnitude could be equal to zero kilometers, depending on
how the vectors are oriented.
d) The magnitude could have any value between 2.0 km and 14.0 km,
depending on how the vectors are oriented.
e) No conclusion can be reached without knowing the directions of the
vectors.
3.3.8. Two displacement vectors of magnitudes 21 cm and 79 cm are
added. Which one of the following is the only possible choice for
the magnitude of the resultant?
a) 0 cm
b) 28 cm
c) 37 cm
d) 82 cm
e) 114 cm
3.3.8. Two displacement vectors of magnitudes 21 cm and 79 cm are
added. Which one of the following is the only possible choice for
the magnitude of the resultant?
a) 0 cm
b) 28 cm
c) 37 cm
d) 82 cm
e) 114 cm
3.4.1. During the execution of a play, a football player carries the ball
for a distance of 33 m in the direction 76° north of east. To
determine the number of meters gained on the play, find the
northward component of the ball’s displacement.
a) 8.0 m
b) 16 m
c) 24 m
d) 28 m
e) 32 m
3.4.1. During the execution of a play, a football player carries the ball
for a distance of 33 m in the direction 76° north of east. To
determine the number of meters gained on the play, find the
northward component of the ball’s displacement.
a) 8.0 m
b) 16 m
c) 24 m
d) 28 m
e) 32 m
3.4.2. The city of Denver is located approximately one mile (1.61 km)
above sea level. Assume you are standing on a beach in Los
Angeles, California, at sea level; estimate the angle of the resultant
vector with respect to the horizontal axis between your location in
California and Denver.
a) between 1 and 2
b) between 0.5 and 0.9
c) between 0.11 and 0.45
d) between 0.06 and 0.10
e) less than 0.05
3.4.2. The city of Denver is located approximately one mile (1.61 km)
above sea level. Assume you are standing on a beach in Los
Angeles, California, at sea level; estimate the angle of the resultant
vector with respect to the horizontal axis between your location in
California and Denver.
a) between 1 and 2
b) between 0.5 and 0.9
c) between 0.11 and 0.45
d) between 0.06 and 0.10
e) less than 0.05
3.4.3. Determine the angle  in the right triangle shown.
a) 54.5
b) 62.0
c) 35.5
d) 28.0
e) 41.3
3.4.3. Determine the angle  in the right triangle shown.
a) 54.5
b) 62.0
c) 35.5
d) 28.0
e) 41.3
3.4.4. Determine the length of the side of the right triangle labeled x.
a) 2.22 m
b) 1.73 m
c) 1.80 m
d) 2.14 m
e) 1.95 m
3.4.4. Determine the length of the side of the right triangle labeled x.
a) 2.22 m
b) 1.73 m
c) 1.80 m
d) 2.14 m
e) 1.95 m
3.4.5. Determine the length of the side of the right triangle labeled x.
a) 0.79 km
b) 0.93 km
c) 1.51 km
d) 1.77 km
e) 2.83 km
3.4.5. Determine the length of the side of the right triangle labeled x.
a) 0.79 km
b) 0.93 km
c) 1.51 km
d) 1.77 km
e) 2.83 km
3.4.6. Consider the two vectors shown. Complete the following
statement: The component of vector A along vector B is
a) equal to zero.
b) smaller than B.
c) equal to B.
d) larger than B.
e) perpendicular to vector B .
3.4.6. Consider the two vectors shown. Complete the following
statement: The component of vector A along vector B is
a) equal to zero.
b) smaller than B.
c) equal to B.
d) larger than B.
e) perpendicular to vector B .
3.4.7. In a two-dimensional coordinate system, the angle between the
positive x axis and vector A is . Which one of the following
choices is the expression to determine the x-component of A ?
a) A sin 
b) A tan 
c) A cos 
d) A cos1 
e) A/sin 
3.4.7. In a two-dimensional coordinate system, the angle between the
positive x axis and vector A is . Which one of the following
choices is the expression to determine the x-component of A ?
a) A sin 
b) A tan 
c) A cos 
d) A cos1 
e) A/sin 
3.4.8. In a two-dimensional coordinate system, the angle between the
positive y axis and vector A is . Which one of the following
choices is the expression to determine the x-component of A ?
a) A sin 
b) A tan 
c) A cos 
d) A cos1 
e) A/sin 
3.4.8. In a two-dimensional coordinate system, the angle between the
positive y axis and vector A is . Which one of the following
choices is the expression to determine the x-component of A ?
a) A sin 
b) A tan 
c) A cos 
d) A cos1 
e) A/sin 
3.4.9. An escaped convict runs 1.70 km due east of the prison. He
then runs due north to a friend’s house. If the magnitude of the
convict’s total displacement vector is 2.50 km, what is the
direction of his total displacement vector with respect to due east?
a) 43 south of east
b) 47 north of east
c) 56 north of east
d) 34 south of east
e) 34 north of east
3.4.9. An escaped convict runs 1.70 km due east of the prison. He
then runs due north to a friend’s house. If the magnitude of the
convict’s total displacement vector is 2.50 km, what is the
direction of his total displacement vector with respect to due east?
a) 43 south of east
b) 47 north of east
c) 56 north of east
d) 34 south of east
e) 34 north of east
3.4.10. A displacement vector is 23 km in length and directed 65°
south of east. What are the components of this vector?
Eastward Component
Southward Component
a) 21 km
9.7 km
b) 23 km
23 km
c) 23 km
0 km
d) 9.7 km
21 km
e) 0 km
23 km
3.4.10. A displacement vector is 23 km in length and directed 65°
south of east. What are the components of this vector?
Eastward Component
Southward Component
a) 21 km
9.7 km
b) 23 km
23 km
c) 23 km
0 km
d) 9.7 km
21 km
e) 0 km
23 km
3.6.1. A , B , and, C are vectors. Vectors B and C when added together equal the
vector A . Vector A has a magnitude of 88 units and it is directed at an angle of
44 relative to the x axis as shown. Find the scalar components of vectors B and
C.
Bx
By
Cx
Cy
a)
63
0
0
61
b)
0
61
63
0
c)
63
0
61
0
d)
0
63
0
61
e)
61
0
63
0
3.6.1. A , B , and, C are vectors. Vectors B and C when added together equal the
vector A . Vector A has a magnitude of 88 units and it is directed at an angle of
44 relative to the x axis as shown. Find the scalar components of vectors B and
C.
Bx
By
Cx
Cy
a)
63
0
0
61
b)
0
61
63
0
c)
63
0
61
0
d)
0
63
0
61
e)
61
0
63
0
3.8.1. Consider the various vectors given in the choices below. The
cross product of which pair of vectors is equal to zero?
3.8.1. Consider the various vectors given in the choices below. The
cross product of which pair of vectors is equal to zero?
3.8.2. What is the scalar product, A B , if
A  1.1iˆ  2.0ˆj and B  1.0iˆ  1.0ˆj?
a) zero
b) 0.9
c) 1.1iˆ  2.0ˆj
d) 3.1
e) 0.1iˆ  1.0ˆj
3.8.2. What is the scalar product, A B , if
A  1.1iˆ  2.0ˆj and B  1.0iˆ  1.0ˆj?
a) zero
b) 0.9
c) 1.1iˆ  2.0ˆj
d) 3.1
e) 0.1iˆ  1.0ˆj
3.8.3. What is the vector product, A  B , if
A  2.2iˆ  3.4ˆj and B  4.4iˆ  2.0ˆj?
a) zero
b) 10.6k̂
c) 4.4iˆ  15.0ˆj
d) 19.4k̂
e) 8.3
3.8.3. What is the vector product, A  B , if
A  2.2iˆ  3.4ˆj and B  4.4iˆ  2.0ˆj?
a) zero
b) 10.6k̂
c) 4.4iˆ  15.0ˆj
d) 19.4k̂
e) 8.3
3.8.4. The scalar product of two vectors, A B, can be determined in a
variety of ways. Which one of the following choices is false?
a) A B = AB cos , where  is the smallest angle between the two
vectors.
b) The scalar product is the product of B and the component of A in the
direction of B .
c) The scalar product of these two vectors could be equal to zero.
d) The scalar product is the product of A and the component of B in the
direction of A .
e) The scalar product is equal to the product of the magnitudes of the two
vectors and the sine of the smallest angle between the two vectors.
3.8.4. The scalar product of two vectors, A B, can be determined in a
variety of ways. Which one of the following choices is false?
a) A B = AB cos , where  is the smallest angle between the two
vectors.
b) The scalar product is the product of B and the component of A in the
direction of B .
c) The scalar product of these two vectors could be equal to zero.
d) The scalar product is the product of A and the component of B in the
direction of A .
e) The scalar product is equal to the product of the magnitudes of the two
vectors and the sine of the smallest angle between the two vectors.
3.8.5. The vector product of two vectors is equal to zero, but the
magnitudes of the two vectors are not equal to zero. Which one of
the following statements is true?
a) Based on the definition of the vector product, this situation can
never occur.
b) The two vectors must be perpendicular to each other.
c) The two vectors must be parallel to each other.
d) The two vectors must be unit vectors.
e) This can only be true if the scalar product is also equal to zero.
3.8.5. The vector product of two vectors is equal to zero, but the
magnitudes of the two vectors are not equal to zero. Which one of
the following statements is true?
a) Based on the definition of the vector product, this situation can
never occur.
b) The two vectors must be perpendicular to each other.
c) The two vectors must be parallel to each other.
d) The two vectors must be unit vectors.
e) This can only be true if the scalar product is also equal to zero.
3.8.6. Which of the following vector operations produces a vector as
the result if the magnitudes of all of the vectors are not equal to
zero?
a) A
 B C
b) A B

c) C  B

D
 
e)  A  B  C  D 
d) A B C
3.8.6. Which of the following vector operations produces a vector as
the result if the magnitudes of all of the vectors are not equal to
zero?
a) A
 B C
b) A B

c) C  B

D
 
e)  A  B  C  D 
d) A B C