Question 1

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

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  
?

Accepted Answer

A) 2.0 
B) 3.0 
C) 4.0 
D) 5.0 
E) 6.0 
A) 2.0 
B) 3.0 
C) 4.0 
D) 5.0 
E) 6.0

Question 3

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

Accepted Answer

A) 30° 
B) 60° 
C) 90° 
D) 120° 
E) 150° 
A) 30° 
B) 60° 
C) 90° 
D) 120° 
E) 150°

Question 4

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:

Accepted Answer

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

Question 5

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.

Accepted Answer

Yes.If the y components are of

Question 6

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

Accepted Answer

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

Question 7

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)?

Accepted Answer

A) 247° 
B) 235° 
C) 243° 
D) 216° 
E) 144° 
A) 247° 
B) 235° 
C) 243° 
D) 216° 
E) 144°

Question 8

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?

Accepted Answer

The answer of A vector starts at coordinate (3.0,4.0)and ends...

Question 9

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

Question 10

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

Accepted Answer

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

Question 11

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  
?

Accepted Answer

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

Question 12

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)?

Accepted Answer

A) 225° 
B) 221° 
C) 230° 
D) 236° 
E) 206° 
A) 225° 
B) 221° 
C) 230° 
D) 236° 
E) 206°

Question 13

Given that  
And  
,what is  
?

Accepted Answer

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

Question 14

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  Can be represented as the difference of two vectors:  Which one,if either,is correct?

Accepted Answer

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   . 
E) They are both wrong: Vectors can be moved as long as they keep the same magnitude and direction. 
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   . 
E) They are both wrong: Vectors can be moved as long as they keep the same magnitude and direction.

Question 15

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 16

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

Accepted Answer

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

Question 17

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?

Accepted Answer

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

Question 18

If vector  
Is added to vector  
,the result is  
)If  
Is subtracted from  
,the result is  
)What is the magnitude of  
?

Accepted Answer

A) 5.1 
B) 4.1 
C) 5.4 
D) 5.8 
E) 8.2 
A) 5.1 
B) 4.1 
C) 5.4 
D) 5.8 
E) 8.2

Question 19

Which statement is true about the unit vectors  
,  
And  
?

Accepted Answer

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. 
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 20

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  
?

Accepted Answer

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

Exam 3: Vectors

If And ,what is the direction of the vector ?

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 ?

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

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.

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

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 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?

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

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

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 ?

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)?

Given that And ,what is ?

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?

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

If vector Is added to vector ,the result is )If Is subtracted from ,the result is )What is the magnitude of ?

Which statement is true about the unit vectors , And ?

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 ?

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