Question 1

30° is

Accepted Answer

A) π/10 radians 
B) π/6 radians 
C) 1 radian 
D) π/2 radians 
E) π radians 
A) π/10 radians 
B) π/6 radians 
C) 1 radian 
D) π/2 radians 
E) π radians B

Question 2

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

Accepted Answer

A) 0° 
B) 18° 
C) 25° 
D) 45° 
E) 90° 
A) 0° 
B) 18° 
C) 25° 
D) 45° 
E) 90° B

Question 3

Let   and  $\theta$ $\neq$ 90 °  where  $\theta$ is the angle between   and   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)    E

Question 4

If   = (6 m)   - (8 m)   then   has magnitude:

Accepted Answer

A) -8 m 
B) 8 m 
C) 10 m 
D) 40 m 
E) 56 m 
A) -8 m 
B) 8 m 
C) 10 m 
D) 40 m 
E) 56 m

Question 5

Let   = (2 m)   + (6 m)   - (3 m)   and   = (4 m)   + (2 m)   + (1 m)   .Then   equals:

Accepted Answer

A) (8 m)   + (12 m)
  - (3 m)
  
B) (12 m)   − (14 m)
  - (20 m)
  
C) 23 
D) 17 
E) none of these 
A) (8 m)   + (12 m)
  - (3 m)
  
B) (12 m)   − (14 m)
  - (20 m)
  
C) 23 
D) 17 
E) none of these

Question 6

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 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

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 9

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 10

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 11

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 12

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 13

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 14

The vector   in the diagram is equal to:

Accepted Answer

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

Question 15

A vector in the xy plane has a magnitude of 25 and an x component of 12.The angle it makes with the positive x axis is:

Accepted Answer

A) 26 $\degree$ 
B) 29 $\degree$ 
C) 61 $\degree$ 
D) 64 $\degree$ 
E) 241 $\degree$ 
A) 26 $\degree$ 
B) 29 $\degree$ 
C) 61 $\degree$ 
D) 64 $\degree$ 
E) 241 $\degree$

Question 16

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 17

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) 0 m 
B) 15 m 
C) 20 m 
D) 25 m 
E) 225 m 
A) 0 m 
B) 15 m 
C) 20 m 
D) 25 m 
E) 225 m

Question 18

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 19

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 ° 
D) the angle between   and
  is 60 ° 
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 ° 
D) the angle between   and
  is 60 ° 
E)    is perpendicular to

Question 20

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) 0 
B) 1 
C) 3 
D) 5 
E) 7 
A) 0 
B) 1 
C) 3 
D) 5 
E) 7

Exam 3: Vectors

30° is

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

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

If = (6 m) - (8 m) then has magnitude:

Let = (2 m) + (6 m) - (3 m) and = (4 m) + (2 m) + (1 m) .Then equals:

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

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

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

The value of is:

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?

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

The value of is:

The vector in the diagram is equal to:

A vector in the xy plane has a magnitude of 25 and an x component of 12.The angle it makes with the positive x axis is:

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

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 vector is:

If and neither nor vanish, then:

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

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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: