1. Vectors Tip or head: D Tail: C
Vector 𝐶𝐷 is NOT equivalent to vector 𝐷𝐶

2. Vectors

3. Vectors Example: 𝑢 = <4, −2> Notation: <𝑢 1 , 𝑢 2 >
<𝑢 𝑥 , 𝑢 𝑦 >
Draw equivalent vectors
Find its length, magnitude, norm, or absolute value

4. Operations with Vectors: addition
𝐴𝐵 + 𝐵𝐶
“Tip to tail”
𝐵𝐶 + 𝐵𝐴 ???

5. Operations with Vectors: addition
𝒖= <3,−2>
𝒗= <−4,−6>
𝒖+𝒗=

6. Operations with Vectors: scalar multiplication
How do 𝟓 𝒗 and 𝒗 compare?
𝑣 = <3,2>
5 𝑣 =
− 𝑣 =

7. Operations with Vectors: scalar multiplication
How do − 𝒗 and 𝒗 compare?
𝑣 = <3,2>
5 𝑣 =
− 𝑣 =

8. Operations with Vectors
𝑢 =<3,−2>
𝑣 =<−4,−2>
3 𝑢 −6 𝑣 =

9. Unit Vectors

10. Unit Vectors: rewrite
𝑢 = <3, 2>
In general:

11. Unit Vectors: rewrite
𝒗= <4, 11,−5> =

12. Unit Vectors
Write a unit vector with the same direction as 𝒘= <−2, 5>