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Halliday/Resnick/Walker Fundamentals of Physics 8 th edition Classroom Response System Questions Chapter 3 Vectors Reading Questions
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Halliday/Resnick/Walker
Fundamentals of Physics 8th edition
Classroom Response System Questions
Chapter 3 Vectors
Reading Questions
3.2.1. Which of the following parameters, if any, is not a vector?
a) acceleration
b) displacement
c) average velocity
d) all are vectors
e) none are vectors
3.2.1. Which of the following parameters, if any, is not a vector?
a) acceleration
b) displacement
c) average velocity
d) all are vectors
e) none are vectors
3.2.2. Which of the following parameters, if any, is not a scalar
quantity?
a) temperature
b) distance
c) average speed
d) instantaneous velocity
e) all are scalars
3.2.2. Which of the following parameters, if any, is not a scalar
quantity?
a) temperature
b) distance
c) average speed
d) instantaneous velocity
e) all are scalars
3.2.3. Which one of the following statements is true concerning scalar
quantities?
a) Scalar quantities have both magnitude and direction.
b) Scalar quantities must be represented by base units.
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.
3.2.3. Which one of the following statements is true concerning scalar
quantities?
a) Scalar quantities have both magnitude and direction.
b) Scalar quantities must be represented by base units.
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.
3.2.4. Which one of the following quantities is a vector quantity?
a) the age of the pyramids in Egypt
b) the mass of a watermelon
c) the sun's pull on the earth
d) the number of people on board an airplane
e) the temperature of molten lava
3.2.4. Which one of the following quantities is a vector quantity?
a) the age of the pyramids in Egypt
b) the mass of a watermelon
c) the sun's pull on the earth
d) the number of people on board an airplane
e) the temperature of molten lava
3.2.5. Which one of the following situations involves a vector
quantity?
a) The velocity of the rocket was 325 m/s, due east.
b) The overnight low temperature in Toronto was 4.0 C.
c) The volume of the soft drink can is 0.360 liters.
d) The mass of the Martian soil probe was 250 kg.
e) The light took approximately 500 s to travel from the sun to the
earth.
3.2.5. Which one of the following situations involves a vector
quantity?
a) The velocity of the rocket was 325 m/s, due east.
b) The overnight low temperature in Toronto was 4.0 C.
c) The volume of the soft drink can is 0.360 liters.
d) The mass of the Martian soil probe was 250 kg.
e) The light took approximately 500 s to travel from the sun to the
earth.
3.2.6. A vector is represented by an arrow. What is the significance of
the length of the arrow?
a) Long arrows represent velocities and short arrows represent forces.
b) The length of the arrow is proportional to the magnitude of the
vector.
c) Short arrows represent accelerations and long arrows represent
velocities.
d) The length of the arrow indicates its direction.
e) There is no significance to the length of the arrow.
3.2.6. A vector is represented by an arrow. What is the significance of
the length of the arrow?
a) Long arrows represent velocities and short arrows represent forces.
b) The length of the arrow is proportional to the magnitude of the
vector.
c) Short arrows represent accelerations and long arrows represent
velocities.
d) The length of the arrow indicates its direction.
e) There is no significance to the length of the arrow.
3.3.1. Consider the two vectors represented in the drawing. Which of
the following options is the correct way to add graphically vectors
and ?a
b
3.3.1. Consider the two vectors represented in the drawing. Which of
the following options is the correct way to add graphically vectors
and ?a
b
3.3.2. Consider the two vectors represented in the drawing. Which of
the following options is the correct way to subtract graphically
vectors and ?a
b
3.3.2. Consider the two vectors represented in the drawing. Which of
the following options is the correct way to subtract graphically
vectors and ?a
b
3.3.3. The horizontal and vertical components of vector are and ,
respectively. Which one of the following statements concerning the sum
of the magnitudes of the two component vectors is true?
a) vx + vx = 0
b) The sum of the magnitudes of the two components is greater than the
magnitude of .
c) The sum of the magnitudes of the two components is less than the
magnitude of .
d) The sum of the magnitudes of the two components is equal to the
magnitude of .
e) The sum of the magnitudes of the two components is less than or equal to
magnitude of .
v
xv
yv
v
v
v
v
3.3.3. The horizontal and vertical components of vector are and ,
respectively. Which one of the following statements concerning the sum
of the magnitudes of the two component vectors is true?
a) vx + vx = 0
b) The sum of the magnitudes of the two components is greater than the
magnitude of .
c) The sum of the magnitudes of the two components is less than the
magnitude of .
d) The sum of the magnitudes of the two components is equal to the
magnitude of .
e) The sum of the magnitudes of the two components is less than or equal to
magnitude of .
v
xv
yv
v
v
v
v
3.3.4. The horizontal and vertical components of vector are and ,
respectively. Which one of the following statements concerning the vector sum
of the two component vectors is true?
a) The sum of the magnitudes of the two components is greater than the magnitude
of .
b) The vector sum of the two components is greater than the magnitude of .
c) The vector sum of the two components is less than the magnitude of .
d) The vector sum of the two components is equal to the magnitude of .
e) The vector sum of the two components is less than or equal to the magnitude of .
v
xv
yv
v
v
v
v
v
3.3.4. The horizontal and vertical components of vector are and ,
respectively. Which one of the following statements concerning the vector sum
of the two component vectors is true?
a) The sum of the magnitudes of the two components is greater than the magnitude
of .
b) The vector sum of the two components is greater than the magnitude of .
c) The vector sum of the two components is less than the magnitude of .
d) The vector sum of the two components is equal to the magnitude of .
e) The vector sum of the two components is less than or equal to the magnitude of .
v
xv
yv
v
v
v
v
v
3.4.1. Which one of the following statements concerning vectors and
scalars is false?
a) In calculations, the vector components of a vector may be used in
place of the vector itself.
b) It is possible to use vector components that are not perpendicular.
c) A scalar component may be either positive or negative.
d) A vector that is zero may have components other than zero.
e) Two vectors are equal only if they have the same magnitude and
direction.
3.4.1. Which one of the following statements concerning vectors and
scalars is false?
a) In calculations, the vector components of a vector may be used in
place of the vector itself.
b) It is possible to use vector components that are not perpendicular.
c) A scalar component may be either positive or negative.
d) A vector that is zero may have components other than zero.
e) Two vectors are equal only if they have the same magnitude and
direction.
3.4.2. , , and, are three vectors. Vectors and when added
together equal the vector . In mathematical form, . Which
one of the following statements concerning the components of vectors
and must be true if Ay = 0?
a) The y components of vectors and are both equal to zero.
b) The y components of vectors and when added together equal zero.
c) By Cy = 0 or Cy By = 0
d) Either answer (a) or answer (b) is correct, but never both.
e) Either answer (a) or answer (b) is correct. It is also possible that both are
correct.
A
B
C
B
C
A
A B C
B
C
B
B
C
C
3.4.2. , , and, are three vectors. Vectors and when added
together equal the vector . In mathematical form, . Which
one of the following statements concerning the components of vectors
and must be true if Ay = 0?
a) The y components of vectors and are both equal to zero.
b) The y components of vectors and when added together equal zero.
c) By Cy = 0 or Cy By = 0
d) Either answer (a) or answer (b) is correct, but never both.
e) Either answer (a) or answer (b) is correct. It is also possible that both are
correct.
A
B
C
B
C
A
A B C
B
C
B
B
C
C
3.4.3. Vector has a magnitude of 88 km/h and is directed at 25
relative to the x axis. Which of the following choices indicates the
horizontal and vertical components of vector ?
rx ry
a) +22 km/h +66 km/h
b) +39 km/h +79 km/h
c) +79 km/h +39 km/h
d) +66 km/h +22 km/h
e) +72 km/h +48 km/h
r
r
3.4.3. Vector has a magnitude of 88 km/h and is directed at 25
relative to the x axis. Which of the following choices indicates the
horizontal and vertical components of vector ?
rx ry
a) +22 km/h +66 km/h
b) +39 km/h +79 km/h
c) +79 km/h +39 km/h
d) +66 km/h +22 km/h
e) +72 km/h +48 km/h
r
r
3.4.4. Vector has components ax = 15.0 and ay = 9.0. What is the
approximate magnitude of vector ?
a) 12.0
b) 24.0
c) 10.9
d) 6.87
e) 17.5
a
a
3.4.4. Vector has components ax = 15.0 and ay = 9.0. What is the
approximate magnitude of vector ?
a) 12.0
b) 24.0
c) 10.9
d) 6.87
e) 17.5
a
a
3.4.5. Vector has a horizontal component ax = 15.0 m and makes an
angle = 38.0 with respect to the positive x direction. What is
the magnitude of ay, the vertical component of vector ?
a) 4.46 m
b) 4.65 m
c) 5.02 m
d) 7.97 m
e) 14.3 m
a
a
3.4.5. Vector has a horizontal component ax = 15.0 m and makes an
angle = 38.0 with respect to the positive x direction. What is
the magnitude of ay, the vertical component of vector ?
a) 4.46 m
b) 4.65 m
c) 5.02 m
d) 7.97 m
e) 14.3 m
a
a
3.5.1. Which one of the following statements concerning unit vectors
is true?
a) The magnitude of a unit vector is always equal to 1.
b) A unit vector always points in the direction of motion.
c) The magnitude of a unit vector sometimes equals zero.
d) A unit vector depends on the units of measurement used and is a
method for tracking the units throughout a calculation.
e) Unit vectors are predominantly used in mathematics, but seldom
used in physics.
3.5.1. Which one of the following statements concerning unit vectors
is true?
a) The magnitude of a unit vector is always equal to 1.
b) A unit vector always points in the direction of motion.
c) The magnitude of a unit vector sometimes equals zero.
d) A unit vector depends on the units of measurement used and is a
method for tracking the units throughout a calculation.
e) Unit vectors are predominantly used in mathematics, but seldom
used in physics.
3.5.2. A delivery truck leaves a warehouse and travels 2.60 km north. The truck
makes a right turn and travels 1.33 km east before making another right turn and
then travels 1.45 km south to arrive at its destination. Express the displacement
of the truck from the warehouse using unit vectors, where north is the
direction and east is the direction.
a)
b)
c)
d)
e)
ˆ+j
i
ˆ ˆ1.33i + 1.45jd
ˆ ˆ1.15i + 1.33jd
ˆ ˆ1.33i + 1.15jd
ˆ ˆ1.33i + 2.60jd
ˆ ˆ2.60i + 1.45jd
3.5.2. A delivery truck leaves a warehouse and travels 2.60 km north. The truck
makes a right turn and travels 1.33 km east before making another right turn and
then travels 1.45 km south to arrive at its destination. Express the displacement
of the truck from the warehouse using unit vectors, where north is the
direction and east is the direction.
a)
b)
c)
d)
e)
ˆ+j
i
ˆ ˆ1.33i + 1.45jd
ˆ ˆ1.15i + 1.33jd
ˆ ˆ1.33i + 1.15jd
ˆ ˆ1.33i + 2.60jd
ˆ ˆ2.60i + 1.45jd
3.6.1. Vector has scalar components Ax = 35 m/s and Ay = 15 m/s.
Vector has scalar components Bx = 22 m/s and By = 18 m/s.
Determine the scalar components of vector .
Cx Cy
a) 13 m/s 3 m/s
b) 57 m/s 33 m/s
c) 13 m/s 33 m/s
d) 57 m/s 3 m/s
e) 57 m/s 3 m/s
A
B
C A B
3.6.1. Vector has scalar components Ax = 35 m/s and Ay = 15 m/s.
Vector has scalar components Bx = 22 m/s and By = 18 m/s.
Determine the scalar components of vector .
Cx Cy
a) 13 m/s 3 m/s
b) 57 m/s 33 m/s
c) 13 m/s 33 m/s
d) 57 m/s 3 m/s
e) 57 m/s 3 m/s
A
B
C A B
3.6.2. Vector and vector Determine the
vector that results from the operation .
a)
b)
c)
d)
e)
ˆ ˆ3i + 5jA
ˆ ˆ2i 4 j.B
A B
ˆ ˆi + j
ˆ ˆ5i 9j
ˆ ˆi j
ˆ ˆi + 9j
ˆ ˆ5i + j
3.6.2. Vector and vector Determine the
vector that results from the operation .
a)
b)
c)
d)
e)
ˆ ˆ3i + 5jA
ˆ ˆ2i 4 j.B
A B
ˆ ˆi + j
ˆ ˆ5i 9j
ˆ ˆi j
ˆ ˆi + 9j
ˆ ˆ5i + j
3.7.1. How are the unit vectors chosen for a given coordinate system?
a) The unit vectors are always chosen using the six common
directions of north, east, south, west, upward, and downward.
b) The unit vectors are always chosen to represent the directions with
respect to a printed page with the directions, left, right, upward,
downward, into the page, and out of the page.
c) The unit vectors are chosen in any convenient manner because the
relations of vectors are not dependent on the choice of the origin or
the orientation of the axes, which are perpendicular to one another.
d) The unit vectors are chosen in any convenient manner, regardless
of the orientation of the unit vectors with respect to one another.
3.7.1. How are the unit vectors chosen for a given coordinate system?
a) The unit vectors are always chosen using the six common
directions of north, east, south, west, upward, and downward.
b) The unit vectors are always chosen to represent the directions with
respect to a printed page with the directions, left, right, upward,
downward, into the page, and out of the page.
c) The unit vectors are chosen in any convenient manner because the
relations of vectors are not dependent on the choice of the origin or
the orientation of the axes, which are perpendicular to one another.
d) The unit vectors are chosen in any convenient manner, regardless
of the orientation of the unit vectors with respect to one another.
3.8.1. Which of the following statements concerning the multiplication of a
vector by a scalar is true?
a) A vector cannot be mathematically multiplied by a scalar.
b) When a vector is multiplied by a scalar, the result is a scalar product.
c) When a vector is multiplied by a scalar, the result is a vector product.
d) When a vector is multiplied by a scalar, the result is a vector that is
perpendicular to the original vector.
e) When a vector is multiplied by a scalar, the result is a vector that is
parallel to the original vector.
3.8.1. Which of the following statements concerning the multiplication of a
vector by a scalar is true?
a) A vector cannot be mathematically multiplied by a scalar.
b) When a vector is multiplied by a scalar, the result is a scalar product.
c) When a vector is multiplied by a scalar, the result is a vector product.
d) When a vector is multiplied by a scalar, the result is a vector that is
perpendicular to the original vector.
e) When a vector is multiplied by a scalar, the result is a vector that is
parallel to the original vector.
3.8.2. Which of the following statements concerning the multiplication of a
vector by a number n < 1 is true?
a) A vector cannot be mathematically multiplied by a scalar.
b) The result is a vector that is larger than the original vector and oppositely
directed.
c) The result is a vector that is smaller than the original vector and
oppositely directed.
d) The result is a vector that is larger than the original vector and rotated by
90 counterclockwise.
e) The result is a vector that is smaller than the original vector and rotated
by 90 counterclockwise.
3.8.2. Which of the following statements concerning the multiplication of a
vector by a number n < 1 is true?
a) A vector cannot be mathematically multiplied by a scalar.
b) The result is a vector that is larger than the original vector and oppositely
directed.
c) The result is a vector that is smaller than the original vector and
oppositely directed.
d) The result is a vector that is larger than the original vector and rotated by
90 counterclockwise.
e) The result is a vector that is smaller than the original vector and rotated
by 90 counterclockwise.
3.8.3. In which of the following situations does the scalar product of
two vectors have the largest value?
a) The vectors are perpendicular to each other.
b) The angle between the two vectors is forty five degrees.
c) The angle between the two vectors is sixty degrees.
d) The angle between the two vectors is zero degrees.
e) The angle between the two vectors is ninety degrees.
3.8.3. In which of the following situations does the scalar product of
two vectors have the largest value?
a) The vectors are perpendicular to each other.
b) The angle between the two vectors is forty five degrees.
c) The angle between the two vectors is sixty degrees.
d) The angle between the two vectors is zero degrees.
e) The angle between the two vectors is ninety degrees.
3.8.5. In which of the following situations does the magnitude of the
vector product of two vectors have the largest value?
a) The vectors are parallel with each other.
b) The angle between the two vectors is forty five degrees.
c) The angle between the two vectors is sixty degrees.
d) The angle between the two vectors is zero degrees.
e) The angle between the two vectors is ninety degrees.
3.8.5. In which of the following situations does the magnitude of the
vector product of two vectors have the largest value?
a) The vectors are parallel with each other.
b) The angle between the two vectors is forty five degrees.
c) The angle between the two vectors is sixty degrees.
d) The angle between the two vectors is zero degrees.
e) The angle between the two vectors is ninety degrees.
3.8.6. and are vectors. Vector is directed due west and vector
is directed due north. Which of the following choices correctly
indicates the directions of vectors and ?
a) is directed due west and is directed due north
b) is directed due west and is directed due south
c) is directed due east and is directed due south
d) is directed due east and is directed due north
e) is directed due north and is directed due west
1r
2r
1r
2r
1r
2r
1r
1r
1r
1r
1r
2r
2r
2r
2r
2r
3.8.6. and are vectors. Vector is directed due west and vector
is directed due north. Which of the following choices correctly
indicates the directions of vectors and ?
a) is directed due west and is directed due north
b) is directed due west and is directed due south
c) is directed due east and is directed due south
d) is directed due east and is directed due north
e) is directed due north and is directed due west
1r
2r
1r
2r
1r
2r
1r
1r
1r
1r
1r
2r
2r
2r
2r
2r
3.8.7. Vectors and have different magnitudes and directions.
Which of the following vector operations does not result in a
vector?
a)
b)
c)
d)
e)
a
b
a b
a b
a b
ca db
a b
3.8.7. Vectors and have different magnitudes and directions.
Which of the following vector operations does not result in a
vector?
a)
b)
c)
d)
e)
a
b
a b
a b
a b
ca db
a b
3.8.8. Vector is directed due north. Vector is directed due east.
Determine the direction of the vector product, .
a) due south
b) due west
c) vertically downward
d) vertically upward
e) 45 north of east
A
B
A B
3.8.8. Vector is directed due north. Vector is directed due east.
Determine the direction of the vector product, .
a) due south
b) due west
c) vertically downward
d) vertically upward
e) 45 north of east
A
B
A B
3.8.9. Under what conditions does
a) This situation never occurs.
b) This occurs when the two vectors have the same magnitude.
c) This occurs when the two vectors are perpendicular to one another.
d) This occurs when the two vectors are parallel to one another.
e) This always occurs, regardless of the particular vectors involved.
?A B AB
3.8.9. Under what conditions does
a) This situation never occurs.
b) This occurs when the two vectors have the same magnitude.
c) This occurs when the two vectors are perpendicular to one another.
d) This occurs when the two vectors are parallel to one another.
e) This always occurs, regardless of the particular vectors involved.
?A B AB
