Lecture 2: Dot product and Cross product

Dot Product - tells you how similar two vectors are

Properties:

1. commutative a⋅b=b⋅a

2. a⋅(b⋅c)=(a⋅b)+(a⋅c)

3. a⋅a=‖a‖2≧0 a⋅a=0⇔ a=0

4. a⋅b=‖a‖*‖b‖*cos(θ) ⇒θ=arccos((a⋅b)/(‖a‖*‖b‖))

5. a⋅b=0 ⇔a⟂b

Proof of 4: c=a−b

[diagrams of a and b vectors] …