Deck 3: Vector

Question 1

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

A) I.
B) II.
C) III.
D) IV.
E) None of these

Answer 1

IV.

Question 2

If , then:

A) must be parallel and in the same direction
B) must be parallel and in opposite directions
C) either must be zero
D) the angle between must be 60
E) none of the above is true

Answer 2

none of the above is true

Question 3

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

A) zero
B) 3
C) 12
D) 47
E) 50

Answer 3

12

Question 4

A vector of magnitude 6 and another vector have a resultant of magnitude 12. The 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 5

Four vectors all have the same magnitude. The angle
$\theta$
between adjacent vectors is 45

as shown. The correct vector equation is:

A)
B)
C)
D)
E)

Question 6

Let The magnitude of is:

A) 5.00
B) 5.57
C) 7.00
D) 7.42
E) 8.54

Question 7

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) 26
B) 29 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
C) 61 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
D) 64 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
E) 241 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11

Question 8

If then has magnitude:

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

Question 9

The angle between and the positive x axis is:

A) 29
B) 61 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
C) 119 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
D) 151 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
E) 209 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11

Question 10

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

A) A_x² + A_y² = B_x² + B_y²
B) A_x + A_y = B_x + B_y
C) A_x = B_x and A_y = B_y
D) A_y /A_x = B_y /B_x
E) A_x = A_y and B_x = B_y

Question 11

If and neither vanish, then:

A) are parallel and in the same direction
B) are parallel and in opposite directions
C) the angle between is 45
D) the angle between is 60 11eeda0b_2a90_9dcc_a0ba_2fb180f2f491_TB3150_11
E) is perpendicular to

Question 12

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)
B) 1/2
C)
D) 3/2
E) 3

Question 13

The vector in the diagram is equal to:

A)
B)
C)
D)
E)

Question 14

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:

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

Question 15

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

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

Question 16

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 with the x axis. Its y component is:

A)
B)
C) 6
D) -6
E) 12

Question 17

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

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 18

The vector is:

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

The angle between and the positive x axis is:

A) 29
B) 61 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
C) 151 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
D) 209 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
E) 241 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11

Question 20

If and neither vanish, then:

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

Question 21

The two vectors 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?

A)
B)
C)
D)
E)

Question 22

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:

A) 0
B) 18 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
C) 25 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
D) 45 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
E) 90 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11

Question 23

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

A) L²/2
B) L²
C)
D) 2L²
E) none of these

Question 24

Let
and $\theta$$\neq$ 90

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

A)
B)
C)
D)
E)

Question 25

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 . The component of the longer vector along the line of the shorter is:

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

Question 26

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:

A) 20 m
B) 7.2 m
C) 5.0 m
D) 4.5 m
E) 2.2 m

Question 27

The value of is:

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

Question 28

If

A)
B)
C)
D)
E)

Question 29

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

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 30

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 . The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors, is:

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

Question 31

Let The vector sum is:

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

Question 32

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

A) 0
B) 60 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
C) 70 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
D) 80 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11
E) 90 11eeda0b_600d_655d_a0ba_ed408094ce4a_TB3150_11

Question 33

Let Then equals:

A)
B)
C) 23
D) 17
E) none of these

Question 34

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

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 35

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

A) zero
B) L²
C)
D) 2L²
E) none of these

Question 36

Let The vector difference is:

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

Question 37

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

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

Question 38

The value of is:

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

Question 39

Let The angle between these two vectors is given by:

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