Question 1

The value of   is:

Accepted Answer

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

Question 2

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 C

Question 3

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 A

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

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 6

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 $\degree$ 
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 $\degree$ 
E)  none of the above is true

Question 7

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 8

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 9

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

Question 10

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°

Question 11

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 12

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 13

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 14

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 15

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 16

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

Question 17

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 18

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 19

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

Accepted Answer

A)  1.5 m 
B)  4.5 m 
C)  12 m 
D)  15 m 
E)  20 m 
A)  1.5 m 
B)  4.5 m 
C)  12 m 
D)  15 m 
E)  20 m

Question 20

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

Accepted Answer

A)  29 $\degree$ 
B)  61 $\degree$ 
C)  119 $\degree$ 
D)  151 $\degree$ 
E)  209 $\degree$ 
A)  29 $\degree$ 
B)  61 $\degree$ 
C)  119 $\degree$ 
D)  151 $\degree$ 
E)  209 $\degree$

Exam 3: Vector

The value of is:

Let . The magnitude of is:

If and neither nor vanish, then:

The value of is:

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

If , then:

The vector 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:

30° is

One radian is approximately

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

Which of the following is correct?

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 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:

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

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

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

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

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

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

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