1. notation, magnitude, scaling & addition
Vectors
notation, magnitude, scaling & addition

2. What is a vector?
something that has direction and length (AKA “magnitude”)
an ordered list of numbers
3 2
Like an “arrow” in space
Order matters, these are called “components”

3. 2D Vectors

4. Position vectors

5. How is vector different from a point?
notation: P = (x, y)
means ‘location’
example:
place: E&T A221
time: 10 AM
v = [ 𝑥 𝑦 ] or v = [x y]T
means ‘displacement’
example:
distance: 20 steps toward elevators
duration: length of our class
it happens to be 10 AM – 12:30 PM, but it would be 2.5 hours no matter what time it was scheduled to begin.
Analogy to time…

6. What is the relationship between points and vectors?
space
time
point – point
location – location = distance
time – time = duration
point + vector
location + distance = location
time + duration = time
vector + vector
distance + distance = distance
duration + duration = duration
point + point
location + location = ???
time + time = ???

7. Magnitude of a vector
∆𝑥= 𝑥 2 − 𝑥 1
∆𝑦= 𝑦 2 − 𝑦 1
𝑣 = (∆𝑥) 2 + (∆𝑦) 2

8. Vector addition 𝑣 𝑥 𝑣 𝑦 + 𝑤 𝑥 𝑤 𝑦 = 𝑣 𝑥 + 𝑤 𝑥 𝑣 𝑦 + 𝑤 𝑦
𝑣 𝑥 𝑣 𝑦 𝑤 𝑥 𝑤 𝑦 = 𝑣 𝑥 + 𝑤 𝑥 𝑣 𝑦 + 𝑤 𝑦
−1 = ? ?
“as the crow flies”
“as the crow flies”

9. Scaling vectors
𝛼∙ 𝑣 𝑥 𝑣 𝑦 = 𝛼𝑣 𝑥 𝛼𝑣 𝑦
“stretch & squish”