4.2.8 - FoDS (Vectors)

Question 1

What is meant by a vector in computing

Answer 1

A way of representing spatial information and movement in numerical ways, and that allows random access/modification of its elements by their rank

Question 2

What are the features of a vector

Answer 2

• Magnitude
• Direction
• Initial point

Question 3

What are the ways that a vector can be represented

Answer 3

• A list of numbers
• A function

Question 4

When represented as a list of numbers how can a vector be described

Answer 4

• An n-vector over R or Rⁿ, where n is the dimension of the vector, and R is the number set (Real numbers)

Question 5

What set must all the quantities in the vectors be drawn from

Answer 5

• The same number set e.g. the Real numbers

Question 6

How can a vector be represented as a dictionary

Answer 6

• Where the keys are the rank/dimensions and the values are the magnitudes

Question 7

How is a vector function written

Answer 7

F: S –> R
Where:
F - the function to create a vector
S- the complete set of values
R - the co domain (the potential outcomes)
–> - Maps to

Question 8

What is the convex combination of two vectors u and v

Answer 8

• where two vectors u and v with the same initial point combine (by making a triangle with the last side being a straight line between their tips) to create any 3rd vector that lies on the line connecting the 2 vectors

Question 9

What is the equations for convex combination

Answer 9

αu + βv where α, β
≥ 0 and α + β = 1

Question 10

What is the dot product of u and v

Answer 10

u1v1 + u2v2 where:
- u = (u1,u2)
- v = (v1,v2)

Question 11

What is the application of the dot product

Answer 11

To find the angle between two vectors