Physics-Vectors

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

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

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

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

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

The main difference between an scalar and a vector quantity is: A) Magnitude B) Direction C) Unit

B

The main difference between an scalar and a vector quantity is: A) Magnitude B) Direction C) Unit

B

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

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

C

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

D

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

F

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

T

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°

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

C

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

D

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

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

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

A

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.

B

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.

C

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

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.

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

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.

D

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.

F

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

F

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

F

The product of a vector by a scalar is a vector having the same direction of the original vector but a different magnitude.

F