Vectors in Mathematics: Interactive Learning Quizzes for Year 11

Question 1

Which of the following is not an application of vectors?

Accepted Answer

History

Answer

Physics

Answer

Engineering

Answer

Computer Graphics

Question 2

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Mass

Answer

Temperature

Answer

Energy

Question 3

What is the formula for vector addition?

Accepted Answer

(a_x + b_x, a_y + b_y)

Answer

(a_x - b_x, a_y - b_y)

Answer

(a_x * b_x, a_y * b_y)

Answer

(a_x / b_x, a_y / b_y)

Question 4

Calculate the scalar product of vectors a = (2, -3) and b = (-1, 5).

Accepted Answer

-7

Answer

7

Answer

1

Answer

-1

Question 5

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

Accepted Answer

(3/5, 4/5)

Answer

(4/5, 3/5)

Answer

(5/3, 4/3)

Answer

(4/3, 5/3)

Question 6

Which vector operation is not commutative?

Accepted Answer

Cross product

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 7

A vector is a quantity that has both magnitude and direction. Which of the following is an example of a vector quantity?

Accepted Answer

Speed

Answer

Mass

Answer

Temperature

Answer

Volume

Question 8

To find the magnitude of a vector, you use the formula: |v| = √(x^2 + y^2), where x and y are the components of the vector. Find the magnitude of the vector <2, -3>

Accepted Answer

√13

Answer

1

Answer

5

Answer

13

Question 9

Which of the following operations cannot be performed on vectors?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 10

A unit vector is a vector that has a magnitude of 1. Which of the following is a unit vector?

Accepted Answer

<1, 0>

Answer

<2, 0>

Answer

<3, 0>

Answer

<4, 0>

Question 11

A position vector is a vector that points from the origin to a given point. Find the position vector of a point P with coordinates (3, -2)

Accepted Answer

<3, -2>

Answer

<-3, 2>

Answer

<2, -3>

Answer

<-2, 3>

Question 12

Which operation is NOT valid for vectors?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 13

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

Accepted Answer

7

Answer

1

Answer

5

Answer

9

Question 14

Which operation is undefined for vectors?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 15

Which of the following is not a valid application of vectors?

Accepted Answer

Solving systems of linear equations.

Answer

Describing the motion of an object.

Answer

Calculating the work done by a force.

Answer

Finding the moment of inertia of an object.

Question 16

Calculate the magnitude (or length) of vector A = 3i + 4j. Round your answer to the nearest whole number.

Accepted Answer

7

Answer

1

Answer

5

Answer

12

Question 17

Which of the following operations is NOT defined for vectors?

Accepted Answer

Division

Answer

Addition and subtraction

Answer

Multiplication by a scalar

Answer

Dot product (scalar product)

Question 18

Find the vector equation of the line passing through the points A(-1, 2) and B(3, 4).

Accepted Answer

r = (-1, 2) + t(4, 2)

Answer

r = (-1, 2) + t(2, 4)

Answer

r = (1, -2) + t(4, 2)

Answer

r = (1, -2) + t(2, 4)

Question 19

Calculate the magnitude of the vector (a, b).

Accepted Answer

√(a² + b²)

Answer

a + b

Answer

a - b

Answer

Cannot be determined

Question 20

What is the dot product of two perpendicular vectors?

Accepted Answer

0

Answer

1

Answer

-1

Answer

Cannot be determined

Question 21

Which operation is **not** defined for vectors?

Accepted Answer

Division

Answer

Addition

Answer

Multiplication by a scalar

Answer

Cross product

Question 22

Which of the following is a unit vector?

Accepted Answer

(0, 1)

Answer

(2, 3)

Answer

(1, 2, 3)

Answer

(4, 5, 6)

Question 23

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

Accepted Answer

-5

Answer

5

Answer

11

Answer

-11

Question 24

Determine the angle between the vectors (1, 0) and (0, 1).

Accepted Answer

90°

Answer

0°

Answer

45°

Answer

180°

Question 25

Calculate the magnitude of the vector (2, 3).

Accepted Answer

6

Answer

1

Answer

2

Answer

5

Question 26

Determine the unit vector in the direction of (4, 0).

Accepted Answer

(1, 0)

Answer

(4, 0)

Answer

(-4, 0)

Answer

(0, 4)

Question 27

Calculate the projection of the vector (2, 3) onto the vector (1, 2).

Accepted Answer

(2/5, 3/5)

Answer

(3/5, 2/5)

Answer

(4/5, 6/5)

Answer

(6/5, 4/5)

Question 28

Calculate the cross product of the vectors (2, -1, 3) and (1, 2, -4).

Accepted Answer

(13, -11, -6)

Answer

(-13, 11, 6)

Answer

(6, 11, 13)

Answer

(-6, -11, -13)

Question 29

A boat sails 10 km east, then turns 90 degrees and sails 6 km north. Find the boat's overall displacement using vector addition.

Accepted Answer

11.66 km at 37 degrees north of east

Answer

10 km east and 6 km north

Answer

16 km at 63 degrees north of east

Answer

6 km east and 10 km north

Question 30

A position vector represents the displacement of an object from a fixed origin. Find the position vector of a point with coordinates (2, -3).

Accepted Answer

(2, -3)

Answer

(-3, 2)

Answer

(3, -2)

Answer

(-2, 3)

Question 31

Work done by a force is calculated using the dot product of force and displacement vectors. Find the work done by the force (3, 4) acting on an object moving along the displacement (2, 5).

Accepted Answer

26 J

Answer

14 J

Answer

38 J

Answer

Cannot be determined from the given information

Question 32

Which of the following is NOT a property of vector addition?

Accepted Answer

Scalar multiplication distributes over vector addition

Answer

Commutative

Answer

Associative

Answer

Vector addition is closed under the operation

Question 33

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

Accepted Answer

7

Answer

1

Answer

5

Answer

9

Question 34

Identify the operation that is not commutative for vectors.

Accepted Answer

Dot product

Answer

Addition

Answer

Subtraction

Answer

Multiplication by a scalar

Question 35

Calculate the unit vector in the direction of the vector (3, 4).

Accepted Answer

(3/5, 4/5)

Answer

(4/5, 3/5)

Answer

(5/3, 5/4)

Answer

(5/4, 5/3)

Question 36

Which of the following is a vector quantity?

Accepted Answer

Speed

Answer

Distance

Answer

Temperature

Answer

Time

Question 37

What is the magnitude of the vector a = 2i + 3j + 4k?

Accepted Answer

3√5

Answer

3

Answer

√3

Answer

√15

Question 38

Calculate the magnitude of the vector 3i + 4j.

Accepted Answer

7

Answer

1

Answer

5

Answer

9

Question 39

What is the position vector of a point P with coordinates (3, 4) relative to the origin O?

Accepted Answer

3i + 4j

Answer

4i + 3j

Answer

3i - 4j

Answer

4i - 3j

Question 40

What is the velocity vector of an object that moves with a constant speed of 5 m/s in the direction of the vector 3i + 4j?

Accepted Answer

5(3i + 4j)

Answer

5(4i - 3j)

Answer

5(3i - 4j)

Answer

5(4i + 3j)

Question 41

Which of the following is a unit vector?

Accepted Answer

$\sqrt{2}/2\hat{i} + \sqrt{2}/2\hat{j}$

Answer

$2\hat{i} + \hat{j}$

Answer

$\hat{i} - \hat{j}$

Answer

$3\hat{i}$

Question 42

Which of the following represents a vector with a magnitude of 5 and is parallel to the x-axis?

Accepted Answer

5i

Answer

-5j

Answer

5j

Answer

-5i

Question 43

The displacement vector of an object moving from point A to point B is 4i + 3j. If the object returns to point A, what is the displacement vector for the round trip?

Accepted Answer

0

Answer

4i + 3j

Answer

8i + 6j

Answer

-4i - 3j

Question 44

Determine the angle between **i** = i + j and **j** = -i + j. Give your answer in degrees.

Accepted Answer

90°

Answer

45°

Answer

0°

Question 45

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Mass

Answer

Temperature

Answer

Time

Question 46

Determine the gradient of the vector **l** = 2i + 5j.

Accepted Answer

5/2

Answer

-2/5

Answer

-5/2

Answer

2/5

Question 47

Which of the following is the correct formula for vector addition?

Accepted Answer

a + b

Answer

a x b

Answer

a - b

Answer

a / b

Question 48

Which of the following is a unit vector?

Accepted Answer

a / |a|

Answer

a + b

Answer

a x b

Answer

a - b

Question 49

Which of the following is true about parallel vectors?

Accepted Answer

They have the same direction.

Answer

They have the same magnitude.

Answer

They cannot be added or subtracted.

Answer

They are perpendicular to each other.

Question 50

Which of the following is true about perpendicular vectors?

Accepted Answer

Their scalar product is zero.

Answer

They cannot be added or subtracted.

Answer

They have the same magnitude.

Answer

They are parallel to each other.

Question 51

What is the angle between the vectors (1, 0) and (0, 1)?

Accepted Answer

90 degrees

Answer

0 degrees

Answer

180 degrees

Answer

45 degrees

Question 52

Which of the following is an application of vectors in real life?

Accepted Answer

Describing the motion of an object

Answer

Calculating the volume of a sphere

Answer

Measuring the temperature of a room

Answer

Solving linear equations

Question 53

Find the vector that represents the displacement from the origin to the point (2, -3).

Accepted Answer

(2, -3)

Answer

(3, -2)

Answer

(-2, 3)

Answer

(-3, 2)

Question 54

Which of the following vectors is **parallel** to the vector **i + 2j**?

Accepted Answer

2i + 4j

Answer

-2i - 4j

Answer

-i - 2j

Answer

3i + 6j

Question 55

What is the scalar multiplication of the vector **a** = (3, 4) by -2?

Accepted Answer

(-6, -8)

Answer

(2, 4)

Answer

(4, 6)

Answer

(8, 6)

Question 56

Which of the following is **NOT** a vector quantity?

Accepted Answer

Time

Answer

Displacement

Answer

Force

Answer

Velocity

Question 57

Which of the following operations is **NOT** valid for vectors?

Accepted Answer

Division

Answer

Scalar multiplication

Answer

Addition

Answer

Subtraction

Question 58

Which of the following is a unit vector?

Accepted Answer

v = (1/√2, 1/√2)

Answer

u = (2, 3)

Answer

x = (1, 2, 3)

Answer

w = (0, 1)

Question 59

What is the angle between the vectors u = (1, 0) and v = (0, 1)?

Accepted Answer

90°

Answer

0°

Answer

180°

Answer

45°

Question 60

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

Accepted Answer

Calculating the force acting on an object

Answer

Solving quadratic equations

Answer

Simplifying algebraic expressions

Answer

Finding the area of a triangle

Question 61

What is the position vector of a point P with coordinates (2, 3)?

Accepted Answer

r = 2i + 3j

Answer

r = 2j + 3i

Answer

r = i + j

Answer

r = 3i + 2j

Question 62

Which of the following vectors has a magnitude of 1?

Accepted Answer

i/√2 + j/√2

Answer

2i - 3j

Answer

3i + 4j

Answer

i - j

Question 63

Which of these describes a quantity that has both magnitude and direction?

Accepted Answer

Velocity

Answer

Temperature

Answer

Volume

Answer

Mass

Question 64

What is the vector that represents the position of point P with coordinates (2, 3) from the origin?

Accepted Answer

2i + 3j

Answer

3i + 2j

Answer

i + j

Answer

-2i - 3j