Question 1

The vector   is:

Accepted Answer

A)  greater than   in magnitude 
B)  less than   in magnitude 
C)  in the same direction as   
D)  in the direction opposite to   
E)  perpendicular to   
A)  greater than   in magnitude 
B)  less than   in magnitude 
C)  in the same direction as   
D)  in the direction opposite to   
E)  perpendicular to

Question 2

If   and neither   vanish, then:

Accepted Answer

A)    are parallel and in the same direction 
B)    are parallel and in opposite directions 
C)  the angle between   is 45 $\degree$ 
D)  the angle between   is 60 $\degree$ 
E)    is perpendicular to   
A)    are parallel and in the same direction 
B)    are parallel and in opposite directions 
C)  the angle between   is 45 $\degree$ 
D)  the angle between   is 60 $\degree$ 
E)    is perpendicular to

Question 3

A vector   of magnitude 6 and another vector   have a resultant of magnitude 12. The vector   :

Accepted Answer

A)  must have a magnitude of at least 6 but no more than 18 
B)  may have a magnitude of 20 
C)  cannot have a magnitude greater than 12 
D)  must be perpendicular to   
E)  must be perpendicular to the resultant vector 
A)  must have a magnitude of at least 6 but no more than 18 
B)  may have a magnitude of 20 
C)  cannot have a magnitude greater than 12 
D)  must be perpendicular to   
E)  must be perpendicular to the resultant vector

Question 4

The value of   is:

Accepted Answer

A)  zero 
B)  +1 
C)  -1 
D)  3 
E)    
A)  zero 
B)  +1 
C)  -1 
D)  3 
E)

Question 5

If

Accepted Answer

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

Question 6

If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:

Accepted Answer

A)  the scalar product of the vectors must be negative 
B)  the scalar product of the vectors must be positive 
C)  the vectors must be parallel and in opposite directions 
D)  the vectors must be parallel and in the same direction 
E)  none of the above 
A)  the scalar product of the vectors must be negative 
B)  the scalar product of the vectors must be positive 
C)  the vectors must be parallel and in opposite directions 
D)  the vectors must be parallel and in the same direction 
E)  none of the above

Question 7

A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is:

Accepted Answer

A)  zero 
B)  1 
C)  3 
D)  5 
E)  7 
A)  zero 
B)  1 
C)  3 
D)  5 
E)  7

Question 8

A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x axis and negative y axis and makes an angle of 30   with the x axis. Its y component is:

Accepted Answer

A)    
B)    
C)  6 
D)  -6 
E)  12 
A)    
B)    
C)  6 
D)  -6 
E)  12

Question 9

The two vectors   define a plane (it is the plane of the triangle with both tails at one vertex and each head at one of the other vertices). Which of the following vectors is perpendicular to the plane?

Accepted Answer

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

Question 10

The vectors   ,   , and   are related by   . Which diagram below illustrates this relationship?

Accepted Answer

A)  I. 
B)  II. 
C)  III. 
D)  IV. 
E)  None of these 
A)  I. 
B)  II. 
C)  III. 
D)  IV. 
E)  None of these

Question 11

Let   The magnitude of   is:

Accepted Answer

A)  5.00 
B)  5.57 
C)  7.00 
D)  7.42 
E)  8.54 
A)  5.00 
B)  5.57 
C)  7.00 
D)  7.42 
E)  8.54

Question 12

The vector   in the diagram is equal to:

Accepted Answer

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

Question 13

A certain vector in the xy plane has an x component of 4m and a y component of 10m. It is then rotated in the xy plane so its x component is doubled. Its new y component is about:

Accepted Answer

A)  20 m 
B)  7.2 m 
C)  5.0 m 
D)  4.5 m 
E)  2.2 m 
A)  20 m 
B)  7.2 m 
C)  5.0 m 
D)  4.5 m 
E)  2.2 m

Question 14

Vectors   each have magnitude L. When drawn with their tails at the same point, the angle between them is 30   . The magnitude of   is:

Accepted Answer

A)  L2/2 
B)  L2  
C)    
D)  2L2  
E)  none of these 
A)  L2/2 
B)  L2  
C)    
D)  2L2  
E)  none of these

Question 15

Vectors   each have magnitude L. When drawn with their tails at the same point, the angle between them is 30   . The value of   is:

Accepted Answer

A)  zero 
B)  L2  
C)    
D)  2L2  
E)  none of these 
A)  zero 
B)  L2  
C)    
D)  2L2  
E)  none of these

Question 16

Four vectors   all have the same magnitude. The angle 
$\theta$
 between adjacent vectors is 45
 
 as shown. The correct vector equation is:

Accepted Answer

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

Question 17

If   and neither   vanish, then:

Accepted Answer

A)    are parallel and in the same direction 
B)    are parallel and in opposite directions 
C)  the angle between   is 45   
D)  the angle between   is 60   
E)    is perpendicular to   
A)    are parallel and in the same direction 
B)    are parallel and in opposite directions 
C)  the angle between   is 45   
D)  the angle between   is 60   
E)    is perpendicular to

Question 18

A vector has a component of 10 m in the +x direction, a component of 10 m in the +y direction, and a component of 5 m in the +z direction. The magnitude of this vector is:

Accepted Answer

A)  zero 
B)  15 m 
C)  20 m 
D)  25 m 
E)  225 m 
A)  zero 
B)  15 m 
C)  20 m 
D)  25 m 
E)  225 m

Question 19

The angle between   and the positive x axis is:

Accepted Answer

A)  29   
B)  61   
C)  119   
D)  151   
E)  209   
A)  29   
B)  61   
C)  119   
D)  151   
E)  209

Exam 3: Vector

The vector is:

If and neither vanish, then:

A vector of magnitude 6 and another vector have a resultant of magnitude 12. The vector :

The value of is:

If

If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:

A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is:

A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x axis and negative y axis and makes an angle of 30 with the x axis. Its y component is:

The two vectors define a plane (it is the plane of the triangle with both tails at one vertex and each head at one of the other vertices). Which of the following vectors is perpendicular to the plane?

The vectors , , and are related by . Which diagram below illustrates this relationship?

Let The magnitude of is:

The vector in the diagram is equal to:

A certain vector in the xy plane has an x component of 4m and a y component of 10m. It is then rotated in the xy plane so its x component is doubled. Its new y component is about:

Vectors each have magnitude L. When drawn with their tails at the same point, the angle between them is 30 . The magnitude of is:

Vectors each have magnitude L. When drawn with their tails at the same point, the angle between them is 30 . The value of is:

Four vectors all have the same magnitude. The angle θ\thetaθ between adjacent vectors is 45 as shown. The correct vector equation is:

If and neither vanish, then:

A vector has a component of 10 m in the +x direction, a component of 10 m in the +y direction, and a component of 5 m in the +z direction. The magnitude of this vector is:

The angle between and the positive x axis is:

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