1. Lesson 63 Introduction to Vectors Lesson #1: Vectors are not rays.
Lesson #2: Vectors have more in common with slope.

2. However you will still need to use and understand the symbol.)
Naming Vectors
𝑣 means vector v
𝑞 means vector q
𝑢 means vector u
𝑝 means vector p
𝑤 means vector w
ϴ is an angle, used in later lessons
(Please note that making the symbol for vectors cannot be done in many of the pictures you will see.
However you will still need to use and understand the symbol.)

3. Remember, vectors are NOT rays, the arrow shows direction
Vocabulary
Vector is a quantity that has both magnitude and direction
Magnitude is the length of the vector
Direction is the orientation of the vector, determined by the angle of the vector and the horizontal line
Scalar is magnitude only, no direction
Initial point is the starting point
Terminal point is the endpoint
Remember, vectors are NOT rays, the arrow shows direction

4. Identify the initial and terminal points for each vector
Initial Points
𝑢 point A
𝑣 point C
𝑤 point E
Terminal Points
𝑢 point B
𝑣 point D
𝑤 point F

5. More on naming vectors
When naming vectors, you include the terminal point if applicable:
𝑢 with terminal point B
𝑣 with terminal point D
𝑤 with terminal point F
Vectors can also be named by their points: 𝐴𝐵 𝐶𝐷 𝐸𝐹
Is the order important?
Yes, 𝐸𝐹 & 𝐹𝐸 are different vectors by their direction

6. Find the Magnitude of each vector
𝑢 = 1− −0 2 𝑢 = 𝑢 = 10 𝑎 2 + 𝑏 2 = 𝑐 2 works also 𝑣 = 𝑣 = 20 𝑣 =2 5 𝑤 =4

7. Write the Component Form of each vector
Think 𝑟𝑢𝑛, 𝑟𝑖𝑠𝑒 𝑢 1, 3 𝑣 4,−2 𝑤 −4, 0

8. Any vectors can be added by summing their components
Any vectors can be added by summing their components. The answer is called the resultant vector
𝑢 1, 3 , 𝑣 4,−2 , 𝑤 −4, 0 𝑢 + 𝑣 1, 3 + 4,−2 𝑢 + 𝑣 = 5, 1 𝑢 + 𝑣 + 𝑤 𝑢 + 𝑣 + 𝑤 = 1, 1

9. Equal vectors have the same magnitude and direction
𝑢 , 𝑎 , 𝑏 are equal vectors 1, 3 + 1, 3 + 1, 3 = 3, 9 Or you can do a scalar multiplication 𝟑x1, 𝟑x3 = 3, 9 𝑐 & 𝑑 are opposite vectors −2, −3 + 2, 3 = 0, 0

10. An airplane is flying due north at 450 mph and encounters a headwind of 80 mph south. What is the ground speed of the airplane?
Speed is like magnitude in this problem.
Sketch graph and write component vectors
Find resultant vector 0, 370
Answer question
ground speed is 370 mph

11. What’s our vector, Victor? We have clearance, Clarence.
Any questions?
Roger, Roger.
What’s our vector, Victor?
We have clearance, Clarence.