Question 1

Scalar (dot) product: Determine the angle between the directions of vector   = 3.00   + 1.00   and vector   = -3.00   + 3.00   .

Accepted Answer

A)  26.6° 
B)  30.0° 
C)  88.1° 
D)  117° 
E)  45.2° 
A)  26.6° 
B)  30.0° 
C)  88.1° 
D)  117° 
E)  45.2°

Question 2

Vector (cross) product: If two vectors point in opposite directions, their cross product must be zero.

Accepted Answer

A) True 
 B)False

Question 3

Scalar (dot) product: If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

Accepted Answer

A) True 
 B)False

Question 4

Scalar (dot) product: For the vectors shown in the figure, assume numbers are accurate to two significant figures. The scalar product   ×   is closest to

Accepted Answer

A)  zero. 
B)  16. 
C)  45. 
D)  -16. 
E)  -45. 
A)  zero. 
B)  16. 
C)  45. 
D)  -16. 
E)  -45.

Question 5

Unit vectors: If all the components of a vector are equal to 1, then that vector is a unit vector.

Accepted Answer

A) True 
 B)False

Question 6

Unit vectors: Vectors   and   are shown in the figure. What is |-5.00   + 4.00   |

Accepted Answer

A)  31.8 
B)  -32.0   - 2.00
  
C)  1028 
D)  34.0 
E)  -2.00   - 32.0
  
A)  31.8 
B)  -32.0   - 2.00
  
C)  1028 
D)  34.0 
E)  -2.00   - 32.0

Question 7

Addition and subtraction: If A > B, under what condition is |   -   | = A - B?

Accepted Answer

A)  The statement is never true. 
B)  Vectors   and
  are in opposite directions. 
C)  Vectors   and
  are in the same direction. 
D)  Vectors   and
  are in perpendicular directions. 
E)  The statement is always true. 
A)  The statement is never true. 
B)  Vectors   and
  are in opposite directions. 
C)  Vectors   and
  are in the same direction. 
D)  Vectors   and
  are in perpendicular directions. 
E)  The statement is always true.

Question 8

Unit vectors: Vector   = -3.00   + 3.00   and vector   = 3.00   + 4.00   . What is vector   =   +   ?

Accepted Answer

A)  0.00   + 3.00
  
B)  7.00   + 7.00
  
C)  -3.00   + 7.00
  
D)  0.00   + 7.00
  
E)  -3.00   -3.00
  
A)  0.00   + 3.00
  
B)  7.00   + 7.00
  
C)  -3.00   + 7.00
  
D)  0.00   + 7.00
  
E)  -3.00   -3.00

Question 9

Components: In the figure, the magnitude of vector   is 18.0 units, and the magnitude of vector   is 12.0 units. What vector   must be added to the vectors   and   so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector   by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

Accepted Answer

The answer of Components: In the figure, the magnitude of...

Question 10

Vector (cross) product: If   = -2   - 6   + 2   and   = - 2   -2   - 3   , which of the following numbers is closest to the magnitude of   ×   ?

Accepted Answer

A)  25 
B)  21 
C)  17 
D)  13 
E)  9 
A)  25 
B)  21 
C)  17 
D)  13 
E)  9

Question 11

Addition and subtraction: You walk   to the north, then turn 60° to your right and walk another   How far are you from where you originally started?

Accepted Answer

A)  87 m 
B)  50 m 
C)  94 m 
D)  46 m 
A)  87 m 
B)  50 m 
C)  94 m 
D)  46 m

Question 12

Components: The magnitude of a vector can never be less than the magnitude of one of its components.

Accepted Answer

A) True 
 B)False

Question 13

Components: The components of vector   are Ax = + 3.90 and Ay = -4.00. What is the angle measured counterclockwise from the +x-axis to vector   ?

Accepted Answer

A)  314° 
B)  134° 
C)  224° 
D)  136° 
E)  46.0° 
A)  314° 
B)  134° 
C)  224° 
D)  136° 
E)  46.0°

Question 14

Unit vectors: Vector   = 1.00   + -2.00   and vector   = 3.00   + 4.00   What are the magnitude and direction of vector   =   +   ?

Accepted Answer

A)  7.21 in a direction 33.7° counterclockwise from the positive x axis 
B)  6.00 in a direction 63.4° counterclockwise from the positive x axis 
C)  4.47 in a direction 6.34° counterclockwise from the positive x axis 
D)  4.47 in a direction 26.6° counterclockwise from the positive x axis 
E)  7.21 in a direction 56.3° counterclockwise from the positive x axis 
A)  7.21 in a direction 33.7° counterclockwise from the positive x axis 
B)  6.00 in a direction 63.4° counterclockwise from the positive x axis 
C)  4.47 in a direction 6.34° counterclockwise from the positive x axis 
D)  4.47 in a direction 26.6° counterclockwise from the positive x axis 
E)  7.21 in a direction 56.3° counterclockwise from the positive x axis

Question 15

Scalar (dot) product: The value of the dot product of two vectors depends on the particular coordinate system being used.

Accepted Answer

A) True 
 B)False

Question 16

Unit vectors: If   = + 4   - 2   - 3   and   = - 4   -2   - 3   , which of the following numbers is closest to the magnitude of   -   ?

Accepted Answer

A)  8 
B)  7 
C)  9 
D)  10 
E)  11 
A)  8 
B)  7 
C)  9 
D)  10 
E)  11

Question 17

Scalar (dot) product: Determine the scalar product of   = 6.0   + 4.0   - 2.0   and   = 5.0   - 6.0   - 3.0   .

Accepted Answer

A)  30   + 24
  + 6
  
B)  30   - 24
  + 6
  
C)  12 
D)  60 
E)  undefined 
A)  30   + 24
  + 6
  
B)  30   - 24
  + 6
  
C)  12 
D)  60 
E)  undefined

Question 18

Scalar (dot) product: If two nonzero vectors point in the same direction, their dot product must be zero.

Accepted Answer

A) True 
 B)False

Question 19

Components: As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by

Accepted Answer

A)  180 N at an angle 60.0° with respect to +x-axis. 
B)  60.0 N at an angle 90.0° with respect to +x-axis. 
C)  20.0 N at an angle 34.3° with respect to +x-axis. 
D)  35.5 N at an angle 34.3° with respect to +x-axis. 
E)  40.0 N at an angle 60.0° with respect to +x-axis. 
A)  180 N at an angle 60.0° with respect to +x-axis. 
B)  60.0 N at an angle 90.0° with respect to +x-axis. 
C)  20.0 N at an angle 34.3° with respect to +x-axis. 
D)  35.5 N at an angle 34.3° with respect to +x-axis. 
E)  40.0 N at an angle 60.0° with respect to +x-axis.

Question 20

Vector (cross) product: What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ?

Accepted Answer

A)  -3.00   + 5.00
  - 9.00
  
B)  -5.00   + 2.00
  - 6.00
  
C)  -9.00   - 3.00
  - 3.00
  
D)  -4.00   + 3.00
  - 1.00
  
E)  2.00   - 9.00
  - 2.00
  
A)  -3.00   + 5.00
  - 9.00
  
B)  -5.00   + 2.00
  - 6.00
  
C)  -9.00   - 3.00
  - 3.00
  
D)  -4.00   + 3.00
  - 1.00
  
E)  2.00   - 9.00
  - 2.00

Exam 2: Motion Along a Straight Line

Scalar (dot) product: Determine the angle between the directions of vector = 3.00 + 1.00 and vector = -3.00 + 3.00 .

Vector (cross) product: If two vectors point in opposite directions, their cross product must be zero.

Scalar (dot) product: If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

Scalar (dot) product: For the vectors shown in the figure, assume numbers are accurate to two significant figures. The scalar product × is closest to

Unit vectors: If all the components of a vector are equal to 1, then that vector is a unit vector.

Unit vectors: Vectors and are shown in the figure. What is |-5.00 + 4.00 |

Addition and subtraction: If A > B, under what condition is | - | = A - B?

Unit vectors: Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ?

Vector (cross) product: If = -2 - 6 + 2 and = - 2 -2 - 3 , which of the following numbers is closest to the magnitude of × ?

Addition and subtraction: You walk to the north, then turn 60° to your right and walk another How far are you from where you originally started?

Components: The magnitude of a vector can never be less than the magnitude of one of its components.

Components: The components of vector are Ax = + 3.90 and Ay = -4.00. What is the angle measured counterclockwise from the +x-axis to vector ?

Unit vectors: Vector = 1.00 + -2.00 and vector = 3.00 + 4.00 What are the magnitude and direction of vector = + ?

Scalar (dot) product: The value of the dot product of two vectors depends on the particular coordinate system being used.

Unit vectors: If = + 4 - 2 - 3 and = - 4 -2 - 3 , which of the following numbers is closest to the magnitude of - ?

Scalar (dot) product: Determine the scalar product of = 6.0 + 4.0 - 2.0 and = 5.0 - 6.0 - 3.0 .

Scalar (dot) product: If two nonzero vectors point in the same direction, their dot product must be zero.

Components: As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by

Vector (cross) product: What is the vector product of = 2.00 + 3.00 + 1.00 and = 1.00 - 3.00 - 2.00 ?

Motion in Two or Three Dimensions

Newtons Laws of Motion

Applying Newtons Laws

Work and Kinetic Energy

Potential Energy and Energy Conservation

Momentum, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Fluid Mechanics

Gravitation

Periodic Motion

Mechanical Waves

Sound and Hearing

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

The Second Law of Thermodynamics

Electric Charge and Electric Field

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic Field

Electromagnetic Induction

Inductance

Alternating Current

Electromagnetic Waves Optics

The Nature and Propagation of Light

Geometric Optics

Interference

Filters

Components: The components of vector are A_x = + 3.90 and A_y = -4.00. What is the angle measured counterclockwise from the +x-axis to vector ?

Components: As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are F₁ = 80.0 N, F₂ = 60.0 N, and F₃ = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by