Question 1

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

Accepted Answer

and   .

Question 2

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  
?

Accepted Answer

A) 3.2 
B) 6.3 
C) 9.5 
D) 18 
E) 5 
A) 3.2 
B) 6.3 
C) 9.5 
D) 18 
E) 5 A

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

A) 17° 
B) 73° 
C) 107° 
D) 163° 
E) 100° 
A) 17° 
B) 73° 
C) 107° 
D) 163° 
E) 100°

Question 5

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

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 6

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?

Accepted Answer

A) 35° 
B) 45° 
C) 65° 
D) 55° 
E) 85° 
A) 35° 
B) 45° 
C) 65° 
D) 55° 
E) 85°

Question 7

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

Accepted Answer

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

Question 8

If  
And  
,what is the magnitude of the vector  
?

Accepted Answer

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

Question 9

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:

Accepted Answer

A) 10 cm,90° 
B) 10 cm,180° 
C) 10 cm,4 500° 
D) 20 cm,180° 
E) 20 cm,540° 
A) 10 cm,90° 
B) 10 cm,180° 
C) 10 cm,4 500° 
D) 20 cm,180° 
E) 20 cm,540°

Question 10

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  
?

Accepted Answer

A) 74° 
B) 100° 
C) −81° 
D) −62° 
E) 106° 
A) 74° 
B) 100° 
C) −81° 
D) −62° 
E) 106°

Question 11

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?

Accepted Answer

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. 
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 12

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

Accepted Answer

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

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?

Accepted Answer

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 
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

In what quadrant are both the sine and tangent negative?

Accepted Answer

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

Question 15

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 16

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  
?

Accepted Answer

A) 2.2 
B) 2.5 
C) 4.5 
D) 5.0 
E) 7.0 
A) 2.2 
B) 2.5 
C) 4.5 
D) 5.0 
E) 7.0

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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?

Accepted Answer

A) 27.0 N 
B) 33.2 N 
C) 36.3 N 
D) 23.8 N 
E) 105 N 
A) 27.0 N 
B) 33.2 N 
C) 36.3 N 
D) 23.8 N 
E) 105 N

Question 20

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?

Accepted Answer

A) 0,0 
B) 0,8 
C) 0,12 
D) 400 mi,8 
E) 600 mi,12 
A) 0,0 
B) 0,8 
C) 0,12 
D) 400 mi,8 
E) 600 mi,12

Exam 3: Vectors

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

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 ?

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

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

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?

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

If And ,what is the magnitude of the vector ?

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 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 ?

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?

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

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?

In what quadrant are both the sine and tangent negative?

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 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 ?

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

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

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?

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