Question 1

If = (2 m) − (3 m) and = (1 m) − (2 m), then =

Accepted Answer

A)  (1 m) 
B)  (−1 m) 
C)  (4 m) − (7 m) 
D)  (4 m) + (1 m) 
E)  (−4 m) + (7 m) 
A)  (1 m) 
B)  (−1 m) 
C)  (4 m) − (7 m) 
D)  (4 m) + (1 m) 
E)  (−4 m) + (7 m)

Question 2

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 3

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 4

Vectors and lie in the xy plane. We can deduce that if:

Accepted Answer

A)  Ax2 + Ay2 = Bx2 + By2 
B)  Ax + Ay = Bx + By  
C)  Ax = Bx and Ay = By  
D)  Ay /Ax = By /Bx  
E)  Ax = Ay and Bx = By  
A)  Ax2 + Ay2 = Bx2 + By2 
B)  Ax + Ay = Bx + By  
C)  Ax = Bx and Ay = By  
D)  Ay /Ax = By /Bx  
E)  Ax = Ay and Bx = By

Question 5

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 6

Let = (2 m) + (6 m) - (3 m) and = (4 m) + (2 m) + (1 m). The vector sum 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 7

Let = (1 m) + (2 m) + (2 m) and = (3 m) + (4 m). 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 and 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 and do not lie in the same plane

Question 8

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 9

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 10

Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65 $\degree$. The component of the longer vector along the line of the shorter is:

Accepted Answer

A)  0 
B)  4.2 
C)  6.3 
D)  9.1 
E)  14 
A)  0 
B)  4.2 
C)  6.3 
D)  9.1 
E)  14

Question 11

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 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

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 14

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 $\degree$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 15

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 16

The two vectors (3 m) − (7 m) and (2 m) + (3 m) − (2 m) 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)  (14 m) + (6 m) + (23 m) 
B)  (−14 m) + (6 m) + (23 m) 
C)  (14 m) − (6 m) + (23 m) 
D)  (14 m) + (6 m) − (23 m) 
E)  (14 m) + (6 m) 
A)  (14 m) + (6 m) + (23 m) 
B)  (−14 m) + (6 m) + (23 m) 
C)  (14 m) − (6 m) + (23 m) 
D)  (14 m) + (6 m) − (23 m) 
E)  (14 m) + (6 m)

Question 17

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 $\degree$

Exam 3: Vector

If = (2 m) − (3 m) and = (1 m) − (2 m), then =

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:

The value of is:

Vectors and lie in the xy plane. We can deduce that if:

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

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

Let = (1 m) + (2 m) + (2 m) and = (3 m) + (4 m). The angle between these two vectors is given by:

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:

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

Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65 °\degree° . The component of the longer vector along the line of the shorter is:

If and neither nor vanish, then:

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

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

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 °\degree° with the x axis. Its y component is:

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

The two vectors (3 m) − (7 m) and (2 m) + (3 m) − (2 m) 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 angle between = (25 m) + (45 m) and the positive x axis is:

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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:

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 have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65 $\degree$ . The component of the longer vector along the line of the shorter 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 $\degree$ with the x axis. Its y component is: