Question 1

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   B

Question 2

Let   The angle between these two vectors is given by:

Accepted Answer

A)  cos-1(14/15) 
B)  cos-1(11/225) 
C)  cos-1(104/225) 
D)  cos-1(11/15) 
E)  cannot be found since   do not lie in the same plane 
A)  cos-1(14/15) 
B)  cos-1(11/225) 
C)  cos-1(104/225) 
D)  cos-1(11/15) 
E)  cannot be found since   do not lie in the same plane D

Question 3

The vector   in the diagram is equal to:

Accepted Answer

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

Question 4

Let   The vector sum   is:

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of these 
A)    
B)    
C)    
D)    
E)  none of these

Question 5

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 6

If   then   has magnitude:

Accepted Answer

A)  10 m 
B)  20 m 
C)  30 m 
D)  40 m 
E)  50 m 
A)  10 m 
B)  20 m 
C)  30 m 
D)  40 m 
E)  50 m

Question 7

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 8

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 9

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 10

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 11

Vectors   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 12

Two vectors lie with their tails at the same point. When the angle between them is increased by 20$\degree$ the magnitude of their vector product doubles. The original angle between them was about:

Accepted Answer

A)  0 
B)  18$\degree$ 
C)  25$\degree$ 
D)  45$\degree$ 
E)  90$\degree$ 
A)  0 
B)  18$\degree$ 
C)  25$\degree$ 
D)  45$\degree$ 
E)  90$\degree$

Question 13

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 14

In the diagram,   has magnitude 12 and   has magnitude 8. The x component of   is about:

Accepted Answer

A)  5.5 m 
B)  7.6 m 
C)  12 m 
D)  14 m 
E)  15 m 
A)  5.5 m 
B)  7.6 m 
C)  12 m 
D)  14 m 
E)  15 m

Question 15

Two vectors lie with their tails at the same point. When the angle between them is increased by 20$\degree$ 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$\degree$ 
C)  70$\degree$ 
D)  80$\degree$ 
E)  90$\degree$ 
A)  0 
B)  60$\degree$ 
C)  70$\degree$ 
D)  80$\degree$ 
E)  90$\degree$

Question 16

Let   and   $\theta$ $\neq$90  $\degree$, where   $\theta$ is the angle between   when they are drawn with their tails at the same point. Which of the following is NOT true?

Accepted Answer

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

Question 17

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 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

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

Accepted Answer

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

Question 20

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

Exam 3: Vector

If and neither vanish, then:

Let The angle between these two vectors is given by:

The vector in the diagram is equal to:

Let The vector sum is:

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

If then has magnitude:

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

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:

The vector is:

The value of is:

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

Two vectors lie with their tails at the same point. When the angle between them is increased by 20 °\degree° the magnitude of their vector product doubles. The original angle between them was about:

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

In the diagram, has magnitude 12 and has magnitude 8. The x component of is about:

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

Let and θ\thetaθ ≠\neq= 90 °\degree° , where θ\thetaθ is the angle between when they are drawn with their tails at the same point. Which of the following is NOT true?

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:

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:

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

If and neither vanish, then:

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Two vectors lie with their tails at the same point. When the angle between them is increased by 20 $\degree$ the magnitude of their vector product doubles. The original angle between them was about:

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