Question 1

On occasion, the notation   will be a shorthand notation for   .
-If   and   , what is the direction of the vector   ?

Accepted Answer

A) −49° 
B) −41° 
C) −90° 
D) +49° 
E) +21° 
A) −49° 
B) −41° 
C) −90° 
D) +49° 
E) +21°

Question 2

The vector   has components +5 and +7 along the x and y axes respectively. If the vector is now rotated 90 degrees counterclockwise relative to the original axes, the vector's components are now

Accepted Answer

A) −7; −5. 
B) 7; −5. 
C) −7; 5. 
D) 7; 5. 
E) 7; 0. 
A) −7; −5. 
B) 7; −5. 
C) −7; 5. 
D) 7; 5. 
E) 7; 0.

Question 3

On occasion, the notation   will be a shorthand notation for   .
-A vector   is added to   . The resultant vector is in the positive x direction and has a magnitude equal to   . What is the direction of   ?

Accepted Answer

A) 74° 
B) 100° 
C) −81° 
D) −62° 
E) 106° 
A) 74° 
B) 100° 
C) −81° 
D) −62° 
E) 106°

Question 4

Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What distance separates the two oases?

Accepted Answer

A) 15 km 
B) 48 km 
C) 28 km 
D) 53 km 
E) 55 km 
A) 15 km 
B) 48 km 
C) 28 km 
D) 53 km 
E) 55 km

Question 5

The vector   has components +5 and +7 along the x and y axes, respectively. Along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are

Accepted Answer

A) −7; −5. 
B) 7; −5. 
C) −7; 5. 
D) 7; 5. 
E) 7; 0. 
A) −7; −5. 
B) 7; −5. 
C) −7; 5. 
D) 7; 5. 
E) 7; 0.

Question 6

On occasion, the notation   will be a shorthand notation for   .
-If   = [10 m, 30°] and   = [25 m, 130°], what is the magnitude of the sum of these two vectors?

Accepted Answer

A) 20 m 
B) 35 m 
C) 15 m 
D) 25 m 
E) 50 m 
A) 20 m 
B) 35 m 
C) 15 m 
D) 25 m 
E) 50 m

Question 7

On occasion, the notation   will be a shorthand notation for   .
-Vectors   and   are shown. What is the magnitude of a vector   if   ? ​   ​

Accepted Answer

A) 46 
B) 10 
C) 30 
D) 78 
E) 90 
A) 46 
B) 10 
C) 30 
D) 78 
E) 90

Exam 3: Vectors

On occasion, the notation will be a shorthand notation for . -If and , what is the direction of the vector ?

The vector has components +5 and +7 along the x and y axes respectively. If the vector is now rotated 90 degrees counterclockwise relative to the original axes, the vector's components are now

On occasion, the notation will be a shorthand notation for . -A vector is added to . The resultant vector is in the positive x direction and has a magnitude equal to . What is the direction of ?

Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What distance separates the two oases?

The vector has components +5 and +7 along the x and y axes, respectively. Along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are

On occasion, the notation will be a shorthand notation for . -If = [10 m, 30°] and = [25 m, 130°], what is the magnitude of the sum of these two vectors?

On occasion, the notation will be a shorthand notation for . -Vectors and are shown. What is the magnitude of a vector if ? ​ ​

Getting Started

One-Dimensional Motion

Two- and Three-Dimensional Motion

Newtons Laws of Motion

Applications of Newtons Laws of Motion

Gravity

Conservation of Energy

Energy in Nonisolated Systems

Systems of Particles and Conservation of Momentum

Collisions

Rotation I: Kinematics and Dynamics

Rotation II: a Conservation Approach

Static Equilibrium, Elasticity, and Fracture

Fluids

Oscillations

Traveling Waves

Superposition and Standing Waves

Temperature, Thermal Expansion, and Gas Laws

Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

Electric Forces

Electric Fields

Gausss Law

Electric Potential

Capacitors and Batteries

Current and Resistance

Direct Current Dc Circuits

Magnetic Fields and Forces

Gausss Law for Magnetism and Amperes Law

Faradays Law of Induction

Inductors and Ac Circuits

Maxwells Equations and Electromagnetic Waves

Diffraction and Interference

Applications of the Wave Model

Reflection and Images Formed by Reflection

Refraction and Images Formed by Refraction

Relativity

Filters

On occasion, the notation will be a shorthand notation for . -Vectors and are shown. What is the magnitude of a vector if ?