Question 1

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 2

Two vectors lie with their tails at the same point.When the angle between them is increased by 20° their scalar product has the same magnitude but changes from positive to negative.The original angle between them was:

Accepted Answer

A) 0° 
B) 60° 
C) 70° 
D) 80° 
E) 90° 
A) 0° 
B) 60° 
C) 70° 
D) 80° 
E) 90°

Question 3

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 4

The value of   is:

Accepted Answer

A) 0 
B) +1 
C) -1 
D) 3 
E)    
A) 0 
B) +1 
C) -1 
D) 3 
E)

Question 5

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

Accepted Answer

A) 0 
B) L2  
C)    
D) 2L2  
E) none of these 
A) 0 
B) L2  
C)    
D) 2L2  
E) none of these

Question 6

If the x component of a vector   , in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x axis is:

Accepted Answer

A)    
B) 1/2 
C)    
D) 3/2 
E) 3 
A)    
B) 1/2 
C)    
D) 3/2 
E) 3

Question 7

The angle between   = (25 m)   + (45 m)   and the positive x axis is:

Accepted Answer

A) 29 $\degree$ 
B) 61 $\degree$ 
C) 151 $\degree$ 
D) 209 $\degree$ 
E) 241 $\degree$ 
A) 29 $\degree$ 
B) 61 $\degree$ 
C) 151 $\degree$ 
D) 209 $\degree$ 
E) 241 $\degree$

Question 8

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 9

If   and neither   nor   vanish, then:

Accepted Answer

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

Question 10

If   , then:

Accepted Answer

A)    and
  must be parallel and in the same direction 
B)    and
  must be parallel and in opposite directions 
C) it must be true that either   or
  is zero 
D) the angle between   and
  must be 60 ° 
E) none of the above is true 
A)    and
  must be parallel and in the same direction 
B)    and
  must be parallel and in opposite directions 
C) it must be true that either   or
  is zero 
D) the angle between   and
  must be 60 ° 
E) none of the above is true

Question 11

Let   = (2 m)   + (6 m)   - (3 m)   and   = (4 m)   + (2 m)   + (1 m)   .The vector difference   is:

Accepted Answer

A) (6 m)   + (8 m)
  - (2 m)
  
B) (−2 m)   + (4 m)
  - (4 m)
  
C) (2 m)   − (4 m)
  + (4 m)
  
D) (8 m)   + (12 m)
  - (3 m)
  
E) none of these 
A) (6 m)   + (8 m)
  - (2 m)
  
B) (−2 m)   + (4 m)
  - (4 m)
  
C) (2 m)   − (4 m)
  + (4 m)
  
D) (8 m)   + (12 m)
  - (3 m)
  
E) none of these

Question 12

If the magnitude of the sum of two vectors is greater 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 13

Vectors   and   each have magnitude L.When drawn with their tails at the same point, the angle between them is 30 $\degree$.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 14

Which of the following is correct?

Accepted Answer

A) Multiplying a vector by a scalar gives a scalar result. 
B) Multiplying a vector by a vector always gives a vector result. 
C) Multiplying a vector by a vector never gives a scalar result. 
D) The only type of vector multiplication that gives a scalar result is the dot product. 
E) The only type of vector multiplication that gives a vector result is the cross product. 
A) Multiplying a vector by a scalar gives a scalar result. 
B) Multiplying a vector by a vector always gives a vector result. 
C) Multiplying a vector by a vector never gives a scalar result. 
D) The only type of vector multiplication that gives a scalar result is the dot product. 
E) The only type of vector multiplication that gives a vector result is the cross product.

Question 15

A certain vector in the xy plane has an x component of 4 m and a y component of 10 m.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 16

A vector of magnitude 20 is added to a vector of magnitude 25.The magnitude of this sum can be:

Accepted Answer

A) 0 
B) 3 
C) 12 
D) 47 
E) 50 
A) 0 
B) 3 
C) 12 
D) 47 
E) 50

Question 17

We say that the displacement of a particle is a vector quantity.Our best justification for this assertion is:

Accepted Answer

A) displacement can be specified by a magnitude and a direction 
B) operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments 
C) a displacement is obviously not a scalar 
D) displacement can be specified by three numbers 
E) displacement is associated with motion 
A) displacement can be specified by a magnitude and a direction 
B) operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments 
C) a displacement is obviously not a scalar 
D) displacement can be specified by three numbers 
E) displacement is associated with motion

Question 18

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 19

The result of   is:

Accepted Answer

A) 0 
B) +1 
C)    
D)    
E)    
A) 0 
B) +1 
C)    
D)    
E)

Question 20

One radian is approximately

Accepted Answer

A) 10° 
B) 33° 
C) 57° 
D) 90° 
E) 180° 
A) 10° 
B) 33° 
C) 57° 
D) 90° 
E) 180°

Exam 3: Vectors

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:

Two vectors lie with their tails at the same point.When the angle between them is increased by 20° their scalar product has the same magnitude but changes from positive to negative.The original angle between them was:

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

The value of is:

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

If the x component of a vector , in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x axis is:

The angle between = (25 m) + (45 m) and the positive x axis is:

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

If and neither nor vanish, then:

If , then:

Let = (2 m) + (6 m) - (3 m) and = (4 m) + (2 m) + (1 m) .The vector difference is:

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

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

Which of the following is correct?

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

A vector of magnitude 20 is added to a vector of magnitude 25.The magnitude of this sum can be:

We say that the displacement of a particle is a vector quantity.Our best justification for this assertion is:

Let .The magnitude of is:

The result of is:

One radian is approximately

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