Deck 3: Vectors

Question 1

If
And
,what is the direction of the vector
?

A)−49°
B)−41°
C)−90°
D)+49°
E)+21°

Answer 1

−41°

Question 2

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

Answer 2

6.0

Question 3

If
= [15,80°] and
,what is the magnitude of
?

A)15
B)35
C)32
D)5.0
E)23

Answer 3

32

Question 4

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°

Question 5

Vectors
And
Are shown.What is the magnitude of a vector
If
?

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

Question 6

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°

Question 7

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?

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

Question 8

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
D)18
E)5

Question 9

If
And
,what is the magnitude of the vector
?

A)42
B)22
C)64
D)90
E)13

Question 10

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-1
The three forces shown act on a particle. Use this exhibit to answer the following question(s).
Refer to Exhibit 3-1.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

Question 11

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

Question 12

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

Question 13

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?

A)21° N of W
B)39° W of N
C)69° N of W
D)51° W of N
E)42° W of N

Question 14

On occasion,the notation = [A,θ] will be a shorthand notation for .
If vector Is added to vector ,the result is a third vector that is perpendicular toAnd 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

Question 15

If
= [10 m,30°] and
= [25 m,130°],what is the magnitude of the sum of these two vectors?

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

Question 16

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

Question 17

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°

Question 18

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
?

A)11
B)5.1
C)7.1
D)8.3
E)12.2

Question 19

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°

Question 20

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-1
The three forces shown act on a particle. Use this exhibit to answer the following question(s).
Refer to Exhibit 3-1.What is the direction of the resultant of these three forces?

A)35°
B)45°
C)65°
D)55°
E)85°

Question 21

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-2
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 3-2.What is the child's distance from her starting position?

A)2.8 m
B)3.5 m
C)6.0 m
D)6.9 m
E)12.0 m

Question 22

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-4
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 3-4.The total distance it travels is

A)1000 m.
B)1732 m.
C)2000 m.
D)6298 m.
E)8000 m.

Question 23

The diagram below shows 3 vectors which sum to zero,all of equal length.Which statement below is true?

A)
B)
C)
D)
E)

Question 24

On occasion,the notation = [A,θ] 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°

Question 25

Which statement is true about the unit vectors
,
And
?

A)Their directions are defined by a left-handed coordinate system.
B)The angle between any two is 90 degrees.
C)Each has a length of 1 m.
D)If is directed east and is directed south, points up out of the surface.
E)All of the above.

Question 26

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°

Question 27

On occasion,the notation = [A,θ] will be a shorthand notation for .
Given the statement that
,what can we conclude?

A) and .
B) .
C) and .
D)Any one of the answers above is correct.
E)Only (a)and (b)may be correct.

Question 28

On occasion,the notation = [A,θ] will be a shorthand notation for .
Anthony has added the vectors listed below and gotten the result
)What errors has he made?

A)He lost the minus sign in vector .
B)He read the in as .
C)He lost the minus sign in vector .
D)All of the above are correct.
E)Only (a)and (b)above are correct.

Question 29

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) ;

Question 30

Vectors
And
Have equal magnitudes.Which statement is always true?

A) .
B) .
C) is perpendicular to .
D) is perpendicular to .
E)The magnitude of equals the magnitude of .

Question 31

On occasion,the notation = [A,θ] will be a shorthand notation for .
Given thatAnd ,what is?

A)
B)
C)
D)
E)

Question 32

On occasion,the notation = [A,θ] will be a shorthand notation for .
Dana says any vector Can be represented as the sum of two vectors:
Ardis says any vectorCan be represented as the difference of two vectors: Which one,if either,is correct?

A)They are both wrong: every vector is unique.
B)Dana is correct: Any vector can be represented as a sum of components and not as a difference.
C)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.

Question 33

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-2
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 3-2.The child's displacement is:

A)
B)
C)
D)
E)

Question 34

On occasion,the notation = [A,θ] will be a shorthand notation for .
Given that And ,what is ?

A)
B)
C)
D)
E)

Question 35

Given that
And
,what is
?

A)
B)
C)
D)
E)

Question 36

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-3
The vectors , ,and are shown below. Use this exhibit to answer the following question(s).
Refer to Exhibit 3-3.Which diagram below correctly represents
?

A)
B)
C)
D)
E)

Question 37

On occasion,the notation = [A,θ] will be a shorthand notation for .
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.

Question 38

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-4
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 3-4.The total displacement of the sailboat,the vector sum of its displacements OB,BC,CD and DE,is

A)1732 m,East.
B)2000 m,Northeast.
C)6298 m,East.
D)8000 m,Southeast.
E)8000 m,East.

Question 39

On occasion,the notation = [A,θ] will be a shorthand notation for .
Exhibit 3-3
The vectors , ,and are shown below. Use this exhibit to answer the following question(s).
Refer to Exhibit 3-3.Which diagram below correctly represents
?

A)
B)
C)
D)
E)

Question 40

On occasion,the notation = [A,θ] will be a shorthand notation for .
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

Question 41

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?

Question 42

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.

Question 43

What two vectors are each the same magnitude as and perpendicular to
?

Question 44

In what quadrant are both the sine and tangent negative?

A)1st
B)2nd
C)3rd
D)4th
E)This cannot happen.

Question 45

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.

Question 46

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.

Question 47

Given two non-zero vectors,
And
,such that
,the sum
Satisfies

A) .
B) .
C) .
D) .
E) .