B

The main difference between an scalar and a vector quantity is:

A) Magnitude

B) Direction

C) Unit

A) Magnitude

B) Direction

C) Unit

A

The components of vectors B and C are given as follows:

Bx = -9.2 Cx = -4.5

By = -6.1 Cy = + 4.3

The angle (less than 180 degrees) between vectors B and C , in degrees, is closest to:

A) 77

B) 103

C) 10

D) 170

E) 84

Bx = -9.2 Cx = -4.5

By = -6.1 Cy = + 4.3

The angle (less than 180 degrees) between vectors B and C , in degrees, is closest to:

A) 77

B) 103

C) 10

D) 170

E) 84

A

The magnitude of A is 5.5. Vector A lies in the second quadrant and forms an angle of 34 degrees with the y-axis. The components, Ax and Ay, are closest to:

A) Ax = – 3.1, Ay = + 4.6

B) Ax = + 3.1, Ay = – 4.6

C) Ax = + 4.6, Ay = – 3.1

D) Ax = – 4.6, Ay = + 3.1

E) Ax = – 4.6, Ay = – 3.1

A) Ax = – 3.1, Ay = + 4.6

B) Ax = + 3.1, Ay = – 4.6

C) Ax = + 4.6, Ay = – 3.1

D) Ax = – 4.6, Ay = + 3.1

E) Ax = – 4.6, Ay = – 3.1

D

Vector A has length 4 units and directed to the north. Vector B has length 9 units and is

directed to the south. Calculate the magnitude and direction of A + B .

A) 13 units, south

B) 5 units, north

C) 13 units, north

D) 5 units, south

directed to the south. Calculate the magnitude and direction of A + B .

A) 13 units, south

B) 5 units, north

C) 13 units, north

D) 5 units, south

A

You walk 55 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?

A) 87 m

B) 50 m

C) 94 m

D) 46 m

A) 87 m

B) 50 m

C) 94 m

D) 46 m

A

You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

A) 63° N of E

B) 50° N of E

C) 57° N of E

D) 69° N of E

A) 63° N of E

B) 50° N of E

C) 57° N of E

D) 69° N of E

A

Vector A points to the north and has length A. Vector B points to the east and has length

B = 2.0 A. Find the magnitude of C = 4 A + B in terms of A.

A) 4.5A

B) 6A

C) 3.6A

D) 3.1A

B = 2.0 A. Find the magnitude of C = 4 A + B in terms of A.

A) 4.5A

B) 6A

C) 3.6A

D) 3.1A

B

The main difference between an scalar and a vector quantity is:

A) Magnitude

B) Direction

C) Unit

A) Magnitude

B) Direction

C) Unit

A

Vector A points to the north and has length A. Vector B points to the east and has length

B = 2.5A. Find the direction of C = 7.4 A + B . Express your answer as an angle relative to east.

A) 71° north of east

B) 19° north of east

C) 82° north of east

D) 60° north of east

B = 2.5A. Find the direction of C = 7.4 A + B . Express your answer as an angle relative to east.

A) 71° north of east

B) 19° north of east

C) 82° north of east

D) 60° north of east

D

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 be displacements.

B) A and B must have equal lengths.

C) A and B must point in opposite directions.

D) A and B must point in the same direction.

E) A and B must be at right angles to each other.

A) A and B must be displacements.

B) A and B must have equal lengths.

C) A and B must point in opposite directions.

D) A and B must point in the same direction.

E) A and B must be at right angles to each other.

A

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 statement concerning these vectors is true?

A) A and B must be at right angles to each other.

B) A and B could have any orientation relative to each other.

C) A and B must have equal lengths.

D) A and B must be parallel.

E) A and B could be antiparallel.

A) A and B must be at right angles to each other.

B) A and B could have any orientation relative to each other.

C) A and B must have equal lengths.

D) A and B must be parallel.

E) A and B could be antiparallel.

B

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) A and B have equal magnitudes and point in opposite directions.

B) B and C have equal magnitudes and point in the same direction.

C) B and C have equal magnitudes and point in opposite directions.

D) A and B point in the same direction, but A has twice the magnitude of B.

E) B and C point in the same direction, but C has twice the magnitude of B.

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) A and B have equal magnitudes and point in opposite directions.

B) B and C have equal magnitudes and point in the same direction.

C) B and C have equal magnitudes and point in opposite directions.

D) A and B point in the same direction, but A has twice the magnitude of B.

E) B and C point in the same direction, but C has twice the magnitude of B.

C

What is the angle between the vectors A and -A when they are drawn from a common origin?

A) 0°

B) 90°

C) 180°

D) 270°

E) 360°

A) 0°

B) 90°

C) 180°

D) 270°

E) 360°

D

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

A) 0 cm

B) 28 cm

C) 37 cm

D) 82 cm

E) 114 cm

A

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

A) C = A + B

B) C + A = -B

C) A + B + C = 0

D) C < A + B E) A 2 + B 2 = C 2

C

Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:

A = 2.0 km, east; B = 5.2 km, north; C = 4.9 km, west; D = 3.0 km, south What is the resultant displacement R of the members of the bicycle club: R = A + B + C + D?

A) 0.8 km, south

B) 0.4 km, 45° south of east

C) 3.6 km, 37° north of west

D) 4.0 km, east

E) 4.0 km, south

A = 2.0 km, east; B = 5.2 km, north; C = 4.9 km, west; D = 3.0 km, south What is the resultant displacement R of the members of the bicycle club: R = A + B + C + D?

A) 0.8 km, south

B) 0.4 km, 45° south of east

C) 3.6 km, 37° north of west

D) 4.0 km, east

E) 4.0 km, south

D

A force, F1 , of magnitude 2.0 N and directed due east is exerted on an object. A second

force exerted on the object is F2 = 2.0 N, due north. What is the magnitude and direction of

a third force, F3 , which must be exerted on the object so that the resultant force is zero?

A) 1.4 N, 45° north of east

B) 1.4 N, 45° south of west

C) 2.8 N, 45° north of east

D) 2.8 N, 45° south of west

E) 4.0 N, 45° east of north

force exerted on the object is F2 = 2.0 N, due north. What is the magnitude and direction of

a third force, F3 , which must be exerted on the object so that the resultant force is zero?

A) 1.4 N, 45° north of east

B) 1.4 N, 45° south of west

C) 2.8 N, 45° north of east

D) 2.8 N, 45° south of west

E) 4.0 N, 45° east of north

C

Three vectors A , B , and C have the following x and y components: Ax = 1 m, Ay = 0 m, Bx = 1 m, By = 1 m, Cx = 0 m, Cy = -1 m

According to the graph, how are A , B , and C combined to result in the vector D ?

A) D = A – B – C

B) D = A – B + C

C) D = A + B – C

D) D = A + B + C

E) D = -A + B + C

According to the graph, how are A , B , and C combined to result in the vector D ?

A) D = A – B – C

B) D = A – B + C

C) D = A + B – C

D) D = A + B + C

E) D = -A + B + C

D

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.

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.

D

Use the component method of vector addition to find the resultant of the following three vectors:

A = 56 km, east B = 11 km, 22° south of east C = 88 km, 44° west of south

A) 81 km, 14° west of south

B) 97 km, 62° south of east

C) 52 km, 66° south of east

D) 68 km, 86° south of east

E) 66 km, 7.1° west of south

A = 56 km, east B = 11 km, 22° south of east C = 88 km, 44° west of south

A) 81 km, 14° west of south

B) 97 km, 62° south of east

C) 52 km, 66° south of east

D) 68 km, 86° south of east

E) 66 km, 7.1° west of south

C

A vector F1 has a magnitude of 40.0 units and points 35.0° above the positive x axis. A

second vector F2 has a magnitude of 65.0 units and points in the negative x direction. Use

the component method of vector addition to find the magnitude and direction, relative to the positive x axis, of the resultant F = F1 + F2

A) 53.3 units, 141.8° relative to the +x axis

B) 53.3 units, 52.1° relative to the +x axis

C) 39.6 units, 125.4° relative to the +x axis

D) 39.6 units, 54.6° relative to the +x axis

E) 46.2 units, 136.0° relative to the +x axis

second vector F2 has a magnitude of 65.0 units and points in the negative x direction. Use

the component method of vector addition to find the magnitude and direction, relative to the positive x axis, of the resultant F = F1 + F2

A) 53.3 units, 141.8° relative to the +x axis

B) 53.3 units, 52.1° relative to the +x axis

C) 39.6 units, 125.4° relative to the +x axis

D) 39.6 units, 54.6° relative to the +x axis

E) 46.2 units, 136.0° relative to the +x axis

C

Two vectors A and B , are added together to form the vector C = A + B . The relationship between the magnitudes of these vectors is given by: Cx = A cos 30° + B and Cy = -A sin 30°. Which statement best describes the orientation of these vectors?

A) A points in the negative x direction while B points in the positive y direction.

B) A points in the negative y direction while B points in the positive x direction.

C) A points 30° below the positive x axis while B points in the positive x direction.

D) A points 30° above the positive x axis while B points in the positive x direction.

E) A points 30° above the negative x axis while B points in the positive x direction.

A) A points in the negative x direction while B points in the positive y direction.

B) A points in the negative y direction while B points in the positive x direction.

C) A points 30° below the positive x axis while B points in the positive x direction.

D) A points 30° above the positive x axis while B points in the positive x direction.

E) A points 30° above the negative x axis while B points in the positive x direction.

F

If a vector pointing to the right has a positive magnitude, then one pointing to the left has a negative magnitude.

F

Since vectors always have positive magnitudes, the sum of two vectors must have a magnitude greater than the magnitude of either one of them.

F

The product of a vector by a scalar is a vector having the same direction of the original vector

but a different magnitude.

but a different magnitude.

T

The magnitude of a vector cannot be smaller than the magnitude of any of its components

F

The magnitude of the resultant of two vectors must be greater than or equal to the magnitude

of each of these vectors.

of each of these vectors.

F

The magnitude of the displacement vector from A to B can never be less than the distance

from A to B, but it can be greater than that distance.

from A to B, but it can be greater than that distance.

F

The magnitude of the displacement vector of an object is equal to the distance that object has

moved.

moved.

F

The components of a vector will be the same no matter what coordinate system is used to

express that vector

express that vector