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Florida Gulf Coast University  PHY 2048
Chapter 3—Vectors
MULTIPLE CHOICE
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
Florida Gulf Coast University  PHY 2048
Chapter 3—Vectors
MULTIPLE CHOICE
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
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Florida Gulf Coast University  PHY 2048
Chapter 3—Vectors
MULTIPLE CHOICE
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
1)If = [15, 80?] and , what is the magnitude of ?

 15
 35
 32
d. 5.0
e. 23
 Vectors and are shown. What is the magnitude of a vector if ?
a. 46


b. 10





c. 30





d. 78





e. 90



 If and , what is the magnitude of the vector ?
 42
 22
 64
 90
 13
 If and , what is the direction of the vector ?
a. ?49?
b. ?41?
c. ?90?
d. +49?
e. +21?
 If = [10 m, 30?] and = [25 m, 130?], what is the magnitude of the sum of these two vectors?
 20 m
 35 m
 15 m
 25 m
 50 m
 If = [10 m, 30?] and = [25 m, 130?], what is the direction of the sum of these two vectors?
a. 17?
b. 73?
c. 107?
d. 163?
e. 100?
 A vector, , when added to the vector yields a resultant vector which is in the positive y
direction and has a magnitude equal to that of . What is the magnitude of ? a. 3.2
b. 6.3
c. 9.5
 18
 5
 If vector is added to vector , the result is . If is subtracted from , the result is . What is the magnitude of ?
a. 5.1
b. 4.1
c. 5.4
d. 5.8
e. 8.2
 If = [2.5 cm, 80?], i.e., the magnitude and direction of are 2.5 cm and 80?, = [3.5 cm, 120?], and , what is the direction of (to the nearest degree)?
a. 247?
b. 235?
c. 243?
d. 216?
e. 144?
 If vector is added to vector , the result is . If is subtracted from , the result is .
What is the direction of (to the nearest degree)?
a. 225?
b. 221?
c. 230?
d. 236?
e. 206?
 A vector is added to . The resultant vector is in the positive x direction and has a magnitude equal to . What is the magnitude of ?
 11
b. 5.1
c. 7.1
d. 8.3
e. 12.2
 A vector is added to . The resultant vector is in the positive x direction and has a magnitude equal to that of . What is the direction of ?
a. 74?
b. 100?
c. ?81?
d. ?62?
e. 106?
 If two collinear vectors and are added, the resultant has a magnitude equal to 4.0. If is subtracted from , the resultant has a magnitude equal to 8.0. What is the magnitude of ?
a. 2.0
b. 3.0
c. 4.0
d. 5.0
e. 6.0
 If two collinear vectors and are added, the resultant has a magnitude equal to 4.0. If is subtracted from , the resultant has a magnitude equal to 8.0. What is the magnitude of ?
a. 2.0
b. 3.0
c. 4.0
d. 5.0
e. 6.0
 When vector is added to vector , which has a magnitude of 5.0, the vector representing their sum is perpendicular to and has a magnitude that is twice that of . What is the magnitude of ?
a. 2.2
b. 2.5
c. 4.5
d. 5.0
e. 7.0
 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?
 15 km
 48 km
 28 km
 53 km
 55 km
 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 is the direction from the first oasis to the second oasis?
 21? N of W
 39? W of N
 69? N of W
 51? W of N
 42? W of N
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
Exhibit 31
The three forces shown act on a particle.
Use this exhibit to answer the following question(s).
 Refer to Exhibit 31. What is the magnitude of the resultant of these three forces? a. 27.0 N
b. 33.2 N
c. 36.3 N
d. 23.8 N
e. 105 N
 Refer to Exhibit 31. What is the direction of the resultant of these three forces?
a. 35?
b. 45?
c. 65?
d. 55?
e. 85?
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
 If vector is added to vector , the result is a third vector that is perpendicular to and has a magnitude equal to 3 . What is the ratio of the magnitude of to that of ?
a. 1.8
b. 2.2
c. 3.2
d. 1.3
e. 1.6
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
Exhibit 32
A child starts at one corner of a cubical jungle gym in a playground and climbs up to the diagonally opposite corner. The original corner is the coordinate origin, and the x, y and z axes are oriented along the jungle gym edges. The length of each side is 2 m.
Use this exhibit to answer the following question(s).
 Refer to Exhibit 32. The child's displacement is: a.
b.
c.
d.
e.
 Refer to Exhibit 32. What is the child’s distance from her starting position?
 2.8 m
 3.5 m
 6.0 m
 6.9 m
e. 12.0 m
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
 The displacement of the tip of the 10 cm long minute hand of a clock between 12:15 A.M. and 12:45
P.M. is:
a. 10 cm, 90?
b. 10 cm, 180?
c. 10 cm, 4 500?
d. 20 cm, 180?
e. 20 cm, 540?
 A student decides to spend spring break by driving 50 miles due east, then 50 miles 30 degrees south of east, then 50 miles 30 degrees south of that direction, and to continue to drive 50 miles deviating by 30 degrees each time until he returns to his original position. How far will he drive, and how many vectors must he sum to calculate his displacement?
a. 0, 0
b. 0, 8


c. 0, 12





d. 400 mi, 8





e. 600 mi, 12


 Given that and , what is ? a.
b.
c.
d.
e.
 Given that and , what is ? a.
b.
c.
d.
e.
 Given that and , what is ? a.
b.
c.
d.
e.
 The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true?
 Which statement is true about the unit vectors , and ?
 Their directions are defined by a lefthanded coordinate system.
 The angle between any two is 90 degrees.
 Each has a length of 1 m.
 If is directed east and is directed south, points up out of the surface.
 All of the above.
 Vectors and have equal magnitudes. Which statement is always true?
 .
 .
 is perpendicular to .
 is perpendicular to .
 The magnitude of equals the magnitude of .
 When three vectors, , , and are placed head to tail, the vector sum . If the vectors all have the same magnitude, the angle between the directions of any two adjacent vectors is
a. 30?
b. 60?
c. 90?
d. 120?
e. 150?
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
Exhibit 33
The vectors , , and are shown below.
Use this exhibit to answer the following question(s).
 Refer to Exhibit 33. Which diagram below correctly represents ?
 d.

 e.
c.
 Refer to Exhibit 33. Which diagram below correctly represents ?
 d.

 e.
c.
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
Exhibit 34
The diagram below shows the path taken by a sailboat tacking sideways because it cannot sail directly into the wind.
Use this exhibit to answer the following question(s).
 Refer to Exhibit 34. The total distance it travels is a. 1 000 m.
b. 1 732 m.
c. 2 000 m.
d. 6 298 m.
e. 8 000 m.
 Refer to Exhibit 34. The total displacement of the sailboat, the vector sum of its displacements OB,
BC, CD and DE, is

 1 732 m, East.
 2 000 m, Northeast.
 6 298 m, East.
 8 000 m, Southeast.
 8 000 m, East.
Instructions: On occasion, the notation = [A, ?] will be a shorthand notation for
.
 Dana says any vector can be represented as the sum of two vectors: . Ardis says any
vector can be represented as the difference of two vectors: . Which one, if either, is correct?

 They are both wrong: every vector is unique.
 Dana is correct: Any vector can be represented as a sum of components and not as a difference.
 Ardis is correct: Any vector can be represented as a difference of vector components and
not as a sum.
d.
They are both correct: A difference of vectors is a sum .
e. They are both wrong: Vectors can be moved as long as they keep the same magnitude and direction.
 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
a. ?7; ?5.
b. 7; ?5.
c. ?7; 5.
d. 7; 5.
e. 7; 0.
 Anthony has added the vectors listed below and gotten the result . What errors has he made?

 He lost the minus sign in vector .
 He read the in as .
 He lost the minus sign in vector .
 All of the above are correct.
 Only (a) and (b) above are correct.
 Given the statement that , what can we conclude?
 and .
 .

 and .
 Any one of the answers above is correct.
 Only (a) and (b) may be correct.
 Adding vectors and by the graphical method gives the same result for + and + . If both additions are done graphically from the same origin, the resultant is the vector that goes from the tail of the first vector to the tip of the second vector, i.e, it is represented by a diagonal of the parallelogram formed by showing both additions in the same figure. Note that a parallelogram has 2 diagonals. Keara
says that the sum of two vectors by the parallelogram method is . Shamu says it is . Both used the parallelogram method, but one used the wrong diagonal. Which one of the vector pairs below contains the original two vectors?
a. ;
b. ;
c. ;
d. ;
e. ;
 Given two nonzero vectors, and , such that , the sum satisfies a.
.
b.
.
c.
.
d.
.
e.
.
 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 a. ?7; ?5.
b. 7; ?5.
c. ?7; 5.
d. 7; 5.
e. 7; 0.
 The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are (r, 67.4°). What is the value of the polar coordinate r in this case?
a. 1.92
b. 4.62
c. 12.0
d. 13.0
e. More information is needed.
 In what quadrant are both the sine and tangent negative?
 1st
 2nd
 3rd
 4th
 This cannot happen.
PROBLEM
 Two vectors starting at the same origin have equal and opposite x components. Is it possible for the two vectors to be perpendicular to each other? Justify your answer.
 A vector starts at coordinate (3.0, 4.0) and ends at coordinate (?2.0, 16.0). What are the magnitude and direction of this vector?
 What two vectors are each the same magnitude as and perpendicular to ?