Scalars, Vectors and Tensors Flashcards
Define Scalar
A quantity with size but no directional dependence
What are the property of scalar?
Defined completely by a single number with appropriate units
e.g. length, area, volume, mass, time
For scalars, what happens once the units are stated?
The quantity is denoted entirely by its size or magnitude
Define Vectors
A vector quantity has both magnitude and direction
What are examples of vectors?
- Force
- Velocity
- Acceleration
- Magnetic field strength
How are vectors represented?
Graphically by a line or arrow
What does the length of arrow represent?
Magnitude/size of quantity
What does the direction of the line represent?
The direction in which the vector quantity acts
What does -a represent?
Vector quantity of same magnitude but with opposite direction
For vector addition, how are vectors summed?
Drawing them as a chain then joining endpoints
Define resultant
The sum of a number of vectors
What is the consequence of combined vector effects?
End up where we started because of the particular combination of direction and magnitude
What is the consequence of vectors being circularly distributed?
The vector sum is 0
Why are vectors described mathematically?
Program computers to manipulate it or perform mathematical derivations
how are vectors described mathematically?
Frame of reference based on orthogonal x,y,z axes
Define unit vectors
A vector that has length 1 and has direction along x or y axes
What is vector i?
vector magnitude 1 unit in x direction
What is vector j?
vector magnitude 1 in the y direction
What is vector k?
vector magnitude 1 in the z direction
How can vectors be written as?
Combination of i, j and k
What are 2 types of vector multiplication?
- Scalar Product - dot product
2. Vector Product - cross product
What is fundamental to to theory of how MR works?
Bloch’s equation
What are tensors?
- Come from mathematical physics
- Extension of the idea of vector
- Describe physical situation which depend not only 1 set of direction but another
What does the motion of sailing boat depend on?
- Driving force - wind strength, wind direction
2. Directional property of object - the size of sail, direction of sail
What does diffusion tensor talk about?
Molecular diffusion
What is constrained by microscopic structure?
Random movement of water in tissue
