Section 7 Chapter 43 - Vectors

Question 1

Vector

Answer 1

A quantity with both direction and magnitude

Question 2

How vectors can be represented as a list

Answer 2

[a, b, c] where a, b, c each represent the vectors magnitude along the x, y, z axes

Question 3

How vectors can be represented in terms of sets

Answer 3

A 4-vector over ℝ can be written as ℝ^{<span>4</span>}

Question 4

How a vector can be represented as a function

Answer 4

A vector can be considered as a function that maps {0, 1, 2, 3} to {x, y, z, w}

Question 5

How a vector as a function can be represented in programming

Answer 5

With a dictionary

Question 6

How a vector can be represented visually

Answer 6

A vector can be represented as an arrow from the origin to the point that the vector represents

Question 7

Graphical result of vector addition

Answer 7

Translation

Question 8

Graphical result of scalar-vector multiplication

Answer 8

Scaling

Question 9

Convex combination of two vectors

Answer 9

If u and v are vectors then their convex combination is in the form αu + βv, where α+β

Question 10

How vectors can be used as a parity bit checker

Answer 10

u = [1,1,1,1,1]

v = [0,1,1,0,1]

v dot u (where you replace + with XOR and * with AND) will give you the parity bit to achieve even parity

When you sum the products you are essentially taking the last bit as if you were summing binary