Deck 3: Vector

Question 1

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

A) 29 $\degree$
B) 61 $\degree$
C) 151 $\degree$
D) 209 $\degree$
E) 241 $\degree$

Answer 1

61 $\degree$

Question 2

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

A) 0
B) 3
C) 12
D) 47
E) 50

Answer 2

12

Question 3

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

Answer 3

must have a magnitude of at least 6 but no more than 18

Question 4

30° is

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

Question 5

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:

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

Question 6

If and neither nor vanish, then:

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 7

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 8

One radian is approximately

A) 10°
B) 33°
C) 57°
D) 90°
E) 180°

Question 9

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

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 10

Let . The magnitude of is:

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

Question 11

If , then:

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 12

If and neither nor vanish, then:

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 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:

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

Question 14

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 15

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

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

Question 16

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

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

Question 17

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

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

Question 18

Vectors and 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 19

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

Question 20

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

A)
B)
C)
D)
E)

Question 21

The value of is:

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

Question 22

The value of is:

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

Question 23

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 24

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

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

Question 25

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:

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

Question 26

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 27

Which of the following is correct?

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 28

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

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 29

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:

A) 0°
B) 60 $\degree$
C) 70 $\degree$
D) 80 $\degree$
E) 90 $\degree$

Question 30

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:

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

Question 31

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

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

Question 32

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

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

Question 33

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

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

Question 34

The value of is:

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

Question 35

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

Question 36

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

Question 37

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?

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)