Vectors in Engineering: Interactive Learning Quizzes for Advanced Diploma Students

Question 1

A force of 100 N is applied at a 30° angle to a 20 cm lever. Calculate the moment of the force about the lever's pivot point using the dot product.

Accepted Answer

50 N m

Answer

100 N m

Answer

200 N m

Answer

0 N m

Question 2

Determine the magnitude (length) of the vector (3, 4).

Accepted Answer

7

Answer

5

Answer

12

Answer

25

Question 3

Compute the dot product of the vectors (1, 2) and (3, 4).

Accepted Answer

10

Answer

3

Answer

6

Answer

14

Question 4

Which of the following is NOT a property of vectors?

Accepted Answer

They are always perpendicular to each other.

Answer

They have magnitude and direction.

Answer

They can be added and subtracted.

Answer

They obey the distributive property.

Question 5

Two vectors are said to be perpendicular if their dot product is:

Accepted Answer

Zero

Answer

Equal to the magnitude of one vector

Answer

Equal to the sum of their magnitudes

Answer

One

Question 6

A force of 10 Newtons acts at an angle of 30 degrees to the horizontal. What is the horizontal component of this force?

Accepted Answer

8.66 N

Answer

10 N

Answer

5 N

Answer

17.32 N

Question 7

Two vectors, A and B, have magnitudes of 5 and 10 units respectively. The angle between them is 60 degrees. What is the magnitude of their resultant vector?

Accepted Answer

13.23 units

Answer

10 units

Answer

15 units

Answer

5 units

Question 8

What is the dot product of two perpendicular vectors?

Accepted Answer

Zero

Answer

1

Answer

The product of their magnitudes

Answer

The square of their magnitudes

Question 9

Two vectors are parallel if their cross product is:

Accepted Answer

Zero

Answer

1

Answer

The product of their magnitudes

Answer

A vector perpendicular to both

Question 10

A vector has a magnitude of 10 units and makes an angle of 45 degrees with the horizontal. What is the vertical component of this vector?

Accepted Answer

7.07 units

Answer

10 units

Answer

14.14 units

Answer

5 units

Question 11

Which of the following is NOT a property of the cross product of two vectors?

Accepted Answer

It is commutative

Answer

It is distributive

Answer

It results in a vector

Answer

It is perpendicular to both vectors

Question 12

A force of 10 N acts at an angle of 30 degrees to the horizontal. Resolve the force into its horizontal and vertical components.

Accepted Answer

Horizontal component: 8.66 N, Vertical component: 5 N

Answer

Horizontal component: 5 N, Vertical component: 8.66 N

Answer

Horizontal component: 10 N, Vertical component: 0 N

Question 13

Given two vectors, A = (5, 0) and B = (12, 0), both lying on the x-axis, find the magnitude of their resultant vector.

Accepted Answer

17 units

Answer

7 units

Answer

12 units

Answer

25 units

Question 14

Calculate the dot product of vectors A = (2, 3) and B = (4, -1).

Accepted Answer

5

Answer

-5

Answer

1

Answer

11

Question 15

A force of 500 N is applied to a 200 kg object at an angle of 30 degrees above the horizontal, causing the object to move 10 meters. Calculate the work done by the force.

Accepted Answer

4330 J

Answer

2500 J

Answer

5000 J

Answer

1000 J

Question 16

Find the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6).

Accepted Answer

(-3, 6, -3)

Answer

(-3, 6, 3)

Answer

(3, 6, -3)

Answer

(11, 10, 9)

Question 17

A plane flies at a speed of 500 km/h relative to the air. If there is a wind blowing at 100 km/h from the west, calculate the plane's resultant velocity relative to the ground.

Accepted Answer

510 km/h at an angle of 11.3 degrees north of east

Answer

510 km/h at an angle of 11.3 degrees south of east

Answer

600 km/h at an angle of 11.3 degrees south of east

Answer

600 km/h at an angle of 11.3 degrees north of east

Question 18

A 5 kg object is placed on a 30-degree inclined plane. Determine the component of the gravitational force acting parallel to the incline.

Accepted Answer

24.5 N

Answer

49 N

Answer

12.25 N

Answer

39.2 N

Question 19

Given two forces, F1 = (3, 4) and F2 = (-2, 1), calculate the magnitude of the net force.

Accepted Answer

5.1 N

Answer

2.2 N

Answer

3.6 N

Answer

7.1 N

Question 20

Find the unit vector in the direction of vector A = (3, -4).

Accepted Answer

(0.6, -0.8)

Answer

(0.8, -0.6)

Answer

(3, -4)

Question 21

A 10 kg object is moving with a velocity of 5 m/s. Calculate the momentum of the object.

Accepted Answer

50 kg m/s

Answer

15 kg m/s

Answer

100 kg m/s

Answer

2 kg m/s

Question 22

A force of 10 Newtons acts at an angle of 30 degrees to the horizontal. What is the horizontal component of this force?

Accepted Answer

8.66 N

Answer

5 N

Answer

10 N

Answer

17.32 N

Question 23

Two vectors, A and B, have magnitudes of 5 units and 12 units respectively. If the angle between them is 60 degrees, what is the magnitude of their resultant vector?

Accepted Answer

13 units

Answer

7 units

Answer

17 units

Answer

25 units

Question 24

What is the dot product of vectors A = (2, 3) and B = (-1, 4)?

Accepted Answer

10

Answer

14

Answer

5

Answer

-2

Question 25

A force of 50 Newtons acts on an object, causing it to move 2 meters in the direction of the force. What is the work done by the force?

Accepted Answer

100 J

Answer

25 J

Answer

50 J

Answer

200 J

Question 26

What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?

Accepted Answer

(-3, 6, -3)

Answer

(1, 2, 3)

Answer

(4, 5, 6)

Answer

(10, 10, 10)

Question 27

A torque of 20 Nm is applied to a rigid body. If the moment arm of the force is 4 meters, what is the magnitude of the force?

Accepted Answer

5 N

Answer

10 N

Answer

80 N

Question 28

What is the unit vector in the direction of vector A = (3, -4)?

Accepted Answer

(3/5, -4/5)

Answer

(-3/5, 4/5)

Answer

(3, -4)

Answer

(1/5, -1/5)

Question 29

A plane flies 200 km due east and then 150 km due north. What is the magnitude of the plane's displacement?

Accepted Answer

250 km

Answer

100 km

Answer

225 km

Answer

350 km

Question 30

Two forces, F1 = (2, 3) N and F2 = (-1, 4) N, act on an object. What is the net force acting on the object?

Accepted Answer

(1, 7) N

Answer

(3, 1) N

Answer

(0, 0) N

Answer

(-2, -1) N

Question 31

The angle between two vectors is 90 degrees. What is the value of their dot product?

Accepted Answer

0

Answer

Cannot be determined

Answer

1

Answer

-1