Vectors in Mathematics: Interactive Learning Quizzes for Advanced Diploma in Healthcare

Question 1

Determine the magnitude of the vector <3, -4>.

Accepted Answer

7

Answer

1

Answer

5

Answer

12

Question 2

Find the unit vector in the direction of the vector <6, -8>.

Accepted Answer

<3/5, -4/5>

Answer

<6/10, -8/10>

Answer

<12/14, -16/14>

Answer

<-6/10, 8/10>

Question 3

Find the position vector of a point that is 3 units to the right and 4 units up from the origin.

Accepted Answer

<3, 4>

Answer

<4, 3>

Answer

<-3, -4>

Answer

<-4, -3>

Question 4

Determine the gradient vector of the line passing through points (2, 3) and (5, 7).

Accepted Answer

<3, 4>

Answer

<4, 3>

Answer

<-3, -4>

Answer

<-4, -3>

Question 5

Which physical quantity is a vector?

Accepted Answer

Displacement

Answer

Time

Answer

Speed

Answer

Mass

Question 6

Which of the following operations is undefined for vectors?

Accepted Answer

Division by a vector

Answer

Addition and subtraction

Answer

Multiplication by a scalar

Answer

Cross product

Question 7

What is the definition of the moment of a force F about a point O?

Accepted Answer

The product of the force and the perpendicular distance from the point to the line of action of the force

Answer

The product of the force and the distance from the point to the point of application of the force

Answer

The product of the force and the angle between the force and the vector from the point to the point of application

Answer

The product of the force and the cosine of the angle between the force and the vector from the point to the point of application

Question 8

Which of the following is a vector quantity?

Accepted Answer

Speed

Answer

Mass

Answer

Temperature

Answer

Volume

Question 9

Given two vectors A = 3i + 4j and B = -2i + 5j, what is the magnitude of the vector A + B?

Accepted Answer

13

Answer

1

Answer

5

Answer

9

Question 10

Which property of vectors states that the order of adding two vectors does not affect the result?

Accepted Answer

Commutative property

Answer

Associative property

Answer

Distributive property

Answer

Closure property

Question 11

A force of 100 N acts on a body at an angle of 30 degrees to the horizontal. What is the horizontal component of the force?

Accepted Answer

86.6 N

Answer

50 N

Answer

100 N

Answer

173.2 N

Question 12

Which of the following is a unit vector?

Accepted Answer

i/sqrt(2) + j/sqrt(2)

Answer

2i + 3j

Answer

3i - 4j

Answer

(1/2)i + (1/2)j

Question 13

A car travels 50 km due east and then turns 90 degrees to travel another 30 km due north. Determine the total displacement vector of the car.

Accepted Answer

(80, 30) km

Answer

(30, 80) km

Answer

(50, 50) km

Question 14

A particle moves with a constant velocity. Its initial position vector is (1, 2) and its velocity vector is (3, 4). What is the position vector of the particle after 5 seconds?

Accepted Answer

(14, 18)

Answer

(4, 6)

Answer

(20, 24)

Answer

(5, 10)

Question 15

Which of the following is NOT a valid vector operation?

Accepted Answer

Matrix multiplication

Answer

Scalar product

Answer

Cross product

Answer

Vector addition

Question 16

In healthcare, how are vectors used?

Accepted Answer

They help represent forces acting on the human body.

Answer

They assist in managing patient records.

Answer

They enhance communication between medical professionals.

Answer

They aid in designing surgical instruments.

Question 17

A particle moves from point A to point B. How do we use vectors to describe its velocity?

Accepted Answer

Velocity is defined as the displacement vector divided by the time taken.

Answer

Velocity is a scalar quantity.

Answer

Velocity is independent of the path taken by the particle.

Answer

Velocity is measured in meters only.

Question 18

What is the geometrical interpretation of the dot product of two vectors?

Accepted Answer

It gives the cosine of the angle between the two vectors.

Answer

It gives the scalar product of the two vectors.

Answer

It gives the sum of the magnitudes of the two vectors.

Answer

It gives the difference in magnitudes of the two vectors.

Question 19

Which of the following is a characteristic of a vector?

Accepted Answer

It has both magnitude and direction

Answer

It has only magnitude

Answer

It is a scalar quantity

Answer

It has only direction

Question 20

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

Accepted Answer

90 degrees

Answer

180 degrees

Answer

45 degrees

Answer

0 degrees

Question 21

What is the projection of the vector (3, 4) onto the vector (1, 0)?

Accepted Answer

3

Answer

4

Answer

6

Answer

5

Question 22

What is the magnitude of the vector (3, 4)?

Accepted Answer

5

Answer

25

Answer

7

Answer

12

Question 23

Which of the following operations is NOT defined for vectors?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication by scalars

Question 24

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 25

Which of the following applications of vectors is used in computer graphics?

Accepted Answer

Transformations and rotations

Answer

Force calculations

Answer

Circuit analysis

Answer

Projectile motion

Question 26

What is the position vector of a point that is 3 units to the right and 4 units up on a coordinate plane?

Accepted Answer

(3, 4)

Answer

(-4, -3)

Answer

(4, 3)

Answer

(-3, -4)

Question 27

Which of the following is a vector quantity?

Accepted Answer

Displacement

Answer

Temperature

Answer

Mass

Answer

Time

Question 28

The magnitude of a vector is equal to:

Accepted Answer

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

Answer

The difference of its components

Answer

The sum of its components

Question 29

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

Accepted Answer

v / |v|

Answer

v - |v|

Answer

|v| / v

Answer

v^2 / |v|

Question 30

The scalar product of two vectors is:

Accepted Answer

A scalar quantity equal to the sum of the products of their components

Answer

A vector quantity equal to the sum of the products of their components

Answer

A scalar quantity equal to the difference of the products of their components

Question 31

The vector product of two vectors is:

Accepted Answer

A vector quantity perpendicular to both vectors, with magnitude equal to the area of the parallelogram formed by the vectors

Answer

A scalar quantity equal to the area of the parallelogram formed by the vectors

Question 32

Which of the following applications of vectors is used in GPS navigation?

Accepted Answer

Vector addition

Answer

Vector subtraction

Answer

Vector division

Answer

Vector multiplication

Question 33

A force of 50 N is applied to an object at an angle of 30 degrees above the horizontal. What is the horizontal component of the force?

Accepted Answer

43.3 N

Answer

75 N

Answer

25 N

Answer

100 N

Question 34

A car travels 100 km east and then 50 km north. What is the magnitude of the car's displacement?

Accepted Answer

112 km

Answer

200 km

Answer

150 km

Answer

50 km

Question 35

A projectile is launched with a velocity of 100 m/s at an angle of 45 degrees above the horizontal. What is the vertical component of the projectile's velocity?

Accepted Answer

70.7 m/s

Answer

110 m/s

Answer

90 m/s

Answer

50 m/s

Question 36

A mass of 10 kg is suspended from a spring with a spring constant of 100 N/m. What is the displacement of the mass from its equilibrium position?

Accepted Answer

0.1 m

Answer

0.2 m

Answer

0.5 m

Answer

0.05 m

Question 37

A nurse needs to administer a medication that requires a 10 ml injection at a 45-degree angle. Which of the following best represents the vector describing this injection?

Accepted Answer

A vector with magnitude 10 ml and direction 45 degrees from the horizontal.

Answer

A scalar quantity of 10 ml.

Answer

A vector with magnitude 45 degrees and direction 10 ml.

Question 38

Two forces are acting on a patient's arm: one pulling upwards with 5 N and the other pushing downwards with 3 N. What is the resultant force acting on the arm?

Accepted Answer

2 N upwards.

Answer

2 N downwards.

Answer

8 N downwards.

Question 39

A wheelchair is being pushed 5 meters north and then 12 meters east. What is the magnitude of the resultant displacement?

Accepted Answer

13 meters

Answer

17 meters

Answer

60 meters

Answer

7 meters

Question 40

A patient's heart rate is increasing at a rate of 10 beats per minute. What type of quantity is this?

Accepted Answer

Vector

Answer

None of the above

Answer

Scalar

Answer

Both scalar and vector

Question 41

Which of the following is NOT a valid vector operation?

Accepted Answer

Multiplication of two vectors to produce a scalar.

Answer

Scalar multiplication of a vector.

Answer

Addition of two vectors.

Answer

Subtraction of two vectors.

Question 42

A medical device is being moved 10 cm to the right and then 5 cm downwards. What is the direction of the resultant displacement vector?

Accepted Answer

South-east

Answer

North-west

Answer

North-east

Answer

South-west

Question 43

A patient is receiving an intravenous injection of saline solution at a rate of 5 ml/min. What is the vector quantity in this scenario?

Accepted Answer

The rate of fluid flow.

Answer

The volume of saline solution.

Answer

The time taken for the injection.

Answer

The position of the injection site.

Question 44

A wheelchair is being pushed with a force of 10 N 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

17.32 N

Answer

10 N

Question 45

A medical device emits ultrasound waves that travel at a speed of 1500 m/s in a specific direction. Which of the following best describes this ultrasound wave?

Accepted Answer

A vector with magnitude 1500 m/s and direction of travel.

Answer

A scalar quantity of 1500 m/s.

Answer

A vector with magnitude 1500 m/s and direction perpendicular to the travel path.

Question 46

Two paramedics are carrying a stretcher with a patient. They are applying forces of 50 N and 60 N respectively, at an angle of 120 degrees to each other. What is the magnitude of the resultant force acting on the stretcher?

Accepted Answer

Approximately 51 N

Answer

110 N

Answer

10 N