Vectors and Scalars: Interactive Learning Quizzes for Physics Year 12

Question 1

The dot product of two perpendicular vectors is:

Accepted Answer

0

Answer

1

Answer

The magnitude of either vector

Answer

The sum of the magnitudes of both vectors

Question 2

A force of 10 N acts on an object at an angle of 30° to the horizontal. The horizontal component of the force is:

Accepted Answer

8.66 N

Answer

5 N

Answer

10 N

Answer

17.32 N

Question 3

The magnitude of a vector is calculated by finding:

Accepted Answer

The square root of the sum of the squares of its components

Answer

The length of the vector

Answer

The sum of its components

Answer

The difference of its components

Question 4

Which of the following is a measure of quantity that possesses only magnitude, with no specific direction?

Accepted Answer

Temperature

Answer

Velocity

Answer

Displacement

Answer

Acceleration

Question 5

Which of the following operations is not allowed for vectors?

Accepted Answer

Division by a scalar

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 6

Two vectors are considered parallel if they:

Accepted Answer

Have the same direction

Answer

Have the same magnitude

Answer

Are perpendicular to each other

Answer

Have the same starting point

Question 7

The vector product of two parallel vectors is:

Accepted Answer

Zero

Answer

Equal to the product of their magnitudes

Answer

Equal to the sum of their magnitudes

Answer

Equal to the difference of their magnitudes

Question 8

The position vector of a point P relative to the origin O is:

Accepted Answer

A vector directed from O to P

Answer

A vector directed from P to O

Answer

A vector perpendicular to OP

Answer

A vector parallel to OP

Question 9

The displacement vector of a particle moving from point A to point B is:

Accepted Answer

A vector directed from A to B

Answer

A vector directed from B to A

Answer

A vector parallel to AB

Answer

A vector perpendicular to AB

Question 10

Calculate the magnitude of the vector (3, 4).

Accepted Answer

7

Answer

1

Answer

5

Answer

12

Question 11

Which of the following operations is NOT valid for vectors?

Accepted Answer

Division by a vector

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 12

Which of the following is a scalar quantity that has only magnitude but no direction?

Accepted Answer

Volume

Answer

Displacement

Answer

Velocity

Answer

Acceleration

Question 13

Find the divergence of the vector field F = (x, y, z).

Accepted Answer

3

Answer

0

Answer

1

Answer

x + y + z

Question 14

Which of the following is a scalar quantity?

Accepted Answer

Speed

Answer

Displacement

Answer

Velocity

Answer

Acceleration

Question 15

The magnitude of a vector represents its:

Accepted Answer

Size

Answer

Direction

Answer

Speed

Answer

Acceleration

Question 16

A particle moves 5 meters north and then 3 meters east. What is the magnitude of its displacement?

Accepted Answer

8 meters

Answer

2 meters

Answer

5 meters

Answer

15 meters

Question 17

The scalar product of two vectors is:

Accepted Answer

A scalar

Answer

A vector

Answer

A matrix

Answer

A tensor

Question 18

The gradient of a scalar field represents its:

Accepted Answer

Direction of maximum change

Answer

Rate of change

Answer

Curvature

Answer

Divergence

Question 19

The curl of a vector field represents its:

Accepted Answer

Circulation

Answer

Divergence

Answer

Gradient

Answer

Laplacian

Question 20

Calculate the position vector of point P, which is 5 units to the right and 3 units up from the origin.

Accepted Answer

5i + 3j

Answer

3i + 5j

Answer

5j - 3i

Answer

3j - 5i

Question 21

Which of the following operations is NOT valid for vectors?

Accepted Answer

Division by a vector

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 22

The unit vector in the direction of a vector A is:

Accepted Answer

A/|A|

Answer

A.|A|

Answer

A-|A|

Answer

A+|A|

Question 23

The dot product of two perpendicular vectors is:

Accepted Answer

Zero

Answer

One

Answer

The magnitude of the vectors

Answer

The negative of the magnitude of the vectors

Question 24

Which of the following is the cross product of two antiparallel vectors?

Accepted Answer

Zero

Answer

A vector with a magnitude equal to the product of the magnitudes of the original vectors

Answer

A vector with a magnitude equal to the sum of the magnitudes of the original vectors

Answer

A vector with a direction perpendicular to both original vectors

Question 25

A force of 10 N acts on a body in the positive x-direction. What is the x-component of the force?

Accepted Answer

10 N

Answer

0 N

Answer

5 N

Answer

15 N

Question 26

If two vectors A and B are perpendicular, their dot product is:

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Answer

Indeterminate

Question 27

The vector quantity that describes the change in position of an object is:

Accepted Answer

Displacement

Answer

Velocity

Answer

Acceleration

Answer

Force

Question 28

A particle moves along a straight path with a constant speed. The magnitude of its velocity vector is:

Accepted Answer

Constant

Answer

Zero

Answer

Not constant but parallel to the direction of motion

Answer

Not constant and not parallel to the direction of motion

Question 29

Two forces, F1 = (4 N, 3 N) and F2 = (2 N, 5 N), act on an object. What is the resultant force?

Accepted Answer

(6 N, 8 N)

Answer

(2 N, 8 N)

Answer

(1 N, 9 N)

Answer

(8 N, 2 N)

Question 30

Which of the following is a unit vector?

Accepted Answer

(1, 0, 0)

Answer

(2, 0, 1)

Answer

(3, 4, 5)

Answer

(0, 1, 2)

Question 31

Which of the following is a defining property of a vector quantity?

Accepted Answer

It has both magnitude and direction.

Answer

It can only be added and subtracted.

Answer

It has no magnitude.

Question 32

Which of the following is a scalar quantity?

Accepted Answer

Temperature

Answer

Velocity

Answer

Displacement

Answer

Force

Question 33

The sum of two vectors A and B is represented as:

Accepted Answer

A + B

Answer

A - B

Answer

|A| + |B|

Answer

A/B

Question 34

The dot product of two vectors A and B is a scalar quantity defined as:

Accepted Answer

A . B = |A||B|cosθ

Answer

A . B = |A| + |B|

Answer

A . B = |A||B|sinθ

Question 35

Which of the following is the unit vector in the direction of vector A?

Accepted Answer

A/|A|

Answer

|A| + |B|

Answer

A . B

Answer

|A| - |B|

Question 36

The cross product of two vectors A and B is a vector that is:

Accepted Answer

Perpendicular to both A and B

Answer

Parallel to both A and B

Answer

In the same direction as A

Answer

In the same direction as B

Question 37

The magnitude of the cross product of two vectors A and B is:

Accepted Answer

|A||B|sinθ

Answer

|A||B|cosθ

Answer

|A| - |B|

Answer

|A| + |B|

Question 38

The position vector of a particle moving in a straight line is given as r = (2t, 3t). What is the particle's velocity at t = 1 s?

Accepted Answer

(2, 3) m/s

Answer

(0, 0) m/s

Answer

(1, 1.5) m/s

Answer

(4, 6) m/s

Question 39

Which of the following is a scalar quantity? (A quantity that has only magnitude and no direction)

Accepted Answer

Temperature

Answer

Displacement

Answer

Velocity

Answer

Force

Question 40

The length of a vector represents its:

Accepted Answer

Magnitude

Answer

Unit

Answer

Magnitude and direction

Answer

Direction

Question 41

The result of multiplying a vector by a scalar (a number) is a:

Accepted Answer

Vector

Answer

Matrix

Answer

Scalar

Answer

Tensor

Question 42

Two vectors are said to be perpendicular if their dot product (a mathematical operation that measures the similarity of direction between two vectors) is:

Accepted Answer

Zero

Answer

Equal to the product of their magnitudes

Answer

Negative one

Answer

One

Question 43

The cross product of two vectors (a mathematical operation that results in a vector perpendicular to both original vectors) is a vector that is:

Accepted Answer

Perpendicular to both vectors

Answer

In the same direction as either vector

Answer

Parallel to both vectors

Question 44

Which of the following is an application of vectors in physics?

Accepted Answer

Describing motion

Answer

Calculating volume

Answer

Determining mass

Answer

Measuring temperature

Question 45

A car travels 50 km north and then 30 km east. What is the magnitude (length) of its overall displacement?

Accepted Answer

58 km

Answer

50 km

Answer

80 km

Answer

30 km

Question 46

A force of 100 N is applied at an angle of 30° above the horizontal. What is the vertical component (the component in the vertical direction) of the force?

Accepted Answer

87 N

Answer

173 N

Answer

100 N

Answer

50 N

Question 47

Which of the following is a scalar quantity?

Accepted Answer

Speed

Answer

Acceleration

Answer

Displacement

Answer

Velocity

Question 48

A car travels 10 km east and then 5 km north. What is the magnitude of the car's displacement?

Accepted Answer

11.2 km

Answer

5 km

Answer

15 km

Question 49

Two forces, 5 N and 12 N, act on an object in opposite directions. What is the magnitude of the resultant force?

Accepted Answer

7 N

Answer

17 N

Answer

12 N

Answer

5 N

Question 50

A vector can be represented by:

Accepted Answer

Both magnitude and direction

Answer

Direction only

Answer

Neither magnitude nor direction

Answer

Magnitude only

Question 51

Which of the following is NOT a vector quantity?

Accepted Answer

Temperature

Answer

Velocity

Answer

Momentum

Answer

Force

Question 52

A ball is thrown vertically upwards with an initial velocity of 10 m/s. What is the ball's velocity at its highest point?

Accepted Answer

0 m/s

Answer

Cannot be determined

Answer

10 m/s

Answer

-10 m/s

Question 53

A vector of magnitude 10 units is multiplied by a scalar of 3. What is the magnitude of the resultant vector?

Accepted Answer

30 units

Answer

10 units

Answer

3 units

Answer

13 units

Question 54

Which of the following is the correct representation of a vector on a graph?

Accepted Answer

An arrow with a specific length and direction

Answer

A point on the graph

Answer

A line segment with a specific length

Answer

A number representing the magnitude

Question 55

A plane travels 200 km north and then 300 km east. What is the plane's resultant displacement?

Accepted Answer

361 km at an angle of 56.3° east of north

Answer

500 km at an angle of 45° east of north

Answer

200 km at an angle of 56.3° east of north

Answer

300 km at an angle of 56.3° east of north

Question 56

Which of the following is NOT a characteristic of a vector?

Accepted Answer

It can be added to a scalar

Answer

It has magnitude

Answer

It has direction