Scalars, Vectors and Tensors

Question 1

Define Scalar

Answer 1

A quantity with size but no directional dependence

Question 2

What are the property of scalar?

Answer 2

Defined completely by a single number with appropriate units

e.g. length, area, volume, mass, time

Question 3

For scalars, what happens once the units are stated?

Answer 3

The quantity is denoted entirely by its size or magnitude

Question 4

Define Vectors

Answer 4

A vector quantity has both magnitude and direction

Question 5

What are examples of vectors?

Answer 5

1. Force
2. Velocity
3. Acceleration
4. Magnetic field strength

Question 6

How are vectors represented?

Answer 6

Graphically by a line or arrow

Question 7

What does the length of arrow represent?

Answer 7

Magnitude/size of quantity

Question 8

What does the direction of the line represent?

Answer 8

The direction in which the vector quantity acts

Question 9

What does -a represent?

Answer 9

Vector quantity of same magnitude but with opposite direction

Question 10

For vector addition, how are vectors summed?

Answer 10

Drawing them as a chain then joining endpoints

Question 11

Define resultant

Answer 11

The sum of a number of vectors

Question 12

What is the consequence of combined vector effects?

Answer 12

End up where we started because of the particular combination of direction and magnitude

Question 13

What is the consequence of vectors being circularly distributed?

Answer 13

The vector sum is 0

Question 14

Why are vectors described mathematically?

Answer 14

Program computers to manipulate it or perform mathematical derivations

Question 15

how are vectors described mathematically?

Answer 15

Frame of reference based on orthogonal x,y,z axes

Question 16

Define unit vectors

Answer 16

A vector that has length 1 and has direction along x or y axes

Question 17

What is vector i?

Answer 17

vector magnitude 1 unit in x direction

Question 18

What is vector j?

Answer 18

vector magnitude 1 in the y direction

Question 19

What is vector k?

Answer 19

vector magnitude 1 in the z direction

Question 20

How can vectors be written as?

Answer 20

Combination of i, j and k

Question 21

What are 2 types of vector multiplication?

Answer 21

1. Scalar Product - dot product

2. Vector Product - cross product

Question 22

What is fundamental to to theory of how MR works?

Answer 22

Bloch’s equation

Question 23

What are tensors?

Answer 23

1. Come from mathematical physics
2. Extension of the idea of vector
3. Describe physical situation which depend not only 1 set of direction but another

Question 24

What does the motion of sailing boat depend on?

Answer 24

1. Driving force - wind strength, wind direction

2. Directional property of object - the size of sail, direction of sail

Question 25

What does diffusion tensor talk about?

Answer 25

Molecular diffusion

Question 26

What is constrained by microscopic structure?

Answer 26

Random movement of water in tissue