Lines

Question 1

normal vector

Answer 1

a non-zero vector that is orthogonal to a given line, 𝓁, (or later a vector perpendicular to a given object)
n = [a,b]

Question 2

𝓁

Answer 2

a line in R²

Question 3

P

Answer 3

a point on a line 𝓁

Question 4

p

Answer 4

a position vector for the point P

Question 5

normal vector approach

Answer 5

involves using n • (x-p) = 0 or n • x = n • p
which produces the general equation ax + by = c for a line or R²
this equation is made because x-p is a direction vector and n is a normal vector or a line orthogonal to that vector, ∴ the dot product of these two must be 0

Question 6

d

Answer 6

a direction vector for 𝓁 (≠0)

Question 7

direction vector approach

Answer 7

involves the vector equation x = p + td
where x is the vector [x,y], p is a point on the line, d is a direction vector for the line and ≠0, and t is some constant.

Question 8

parametric equations

Answer 8

equations that split a vector into each of its components in the form of x = p₁ + td₁, y = p₂ + td₂
a vector that satisfies each of these equations can be used. t is a parameter

Question 9

parameter

Answer 9

A variable that is to take different values, thereby giving different values to certain other variables.
ex. t in parametric equations

Question 10

n and d are

Answer 10

orthogonal