Question 1

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 F) B) and E)
G) A) and D)

Question 2

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 F) B) and E)
G) B) and D) A

Question 3

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°F) B) and C)
G) A) and B)

Question 4

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 motionF) A) and E)
G) C) and E)

Question 5

One radian is approximately

Accepted Answer

A)   10°
B)   33°
C)   57°
D)   90°
E)   180°F) A) and B)
G) All of the above

Question 6

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 mF) A) and D)
G) D) and E)

Question 7

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)   7F) B) and E)
G) A) and E)

Question 8

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

Accepted Answer

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

Question 9

Let . The magnitude of is:

Accepted Answer

A)   5.00
B)   5.57
C)   7.00
D)   7.42
E)   8.54F) A) and E)
G) C) and D) C

Question 10

The value of  is:

Accepted Answer

A)   0
B)   +1
C)   -1
D)   3
E)   F) B) and D)
G) A) and E) B

Question 11

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 mF) B) and D)
G) C) and D)

Question 12

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 mF) C) and D)
G) B) and E)

Question 13

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 theseF) B) and D)
G) A) and C)

Question 14

The value of  is:

Accepted Answer

A)   0
B)   +1
C)   -1
D)   3
E)   F) A) and B)
G) B) and E)

Question 15

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.F) None of the above
G) B) and C)

Question 16

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°F) None of the above
G) A) and E)

Question 17

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 theseF) A) and B)
G) A) and C)

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 toF) None of the above
G) B) and E)

Question 19

30° is

Accepted Answer

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

Question 20

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 theseF) B) and E)
G) C) and E)

Exam 3: Vector

If , then:

Correct AnswerverifiedShow Answer

If and neither nor vanish, then:

Correct AnswerverifiedA

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:

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

One radian is approximately

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

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Let . The magnitude of is:

Correct AnswerverifiedC

The value of is:

Correct AnswerverifiedB

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:

Correct AnswerverifiedShow Answer

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:

Correct AnswerverifiedShow Answer

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

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The value of is:

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Which of the following is correct?

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

The vector is:

Correct AnswerverifiedShow Answer

30° is

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

Correct AnswerverifiedShow Answer

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