1. Vectors

2. There are two kinds of quantities…
Vectors have both magnitude and direction
Scalars have magnitude only
What is magnitude?
Size or Amount

3. How you will see magnitude:
Timmy pushes a chair 3 feet forward and 2 feet backward. What is the magnitude of the chair’s displacement?
What is magnitude?
You are solving for displacement, not magnitude
Magnitude means the number & units only

4. Drawing Vectors
Vectors are drawn as Arrows 
head
tail

5. Direction of Vectors A B
The arrow head shows the direction of the vector B

6. Magnitude of Vectors A B
The magnitude of the vector is represented by the length of the arrow B

7. Magnitude of Vectors A 2A
If vector A represents a displacement of three miles to the north… 2A
Then vector 2A, (which means 2 x A) is twice as long, and would represent a displacement of six miles to the north!

8. Opposite Vectors
Opposite vectors have the same length, but opposite direction. A -A

9. Graphical Addition of Vectors: Head to TailB A R
A + B = R
R is called the resultant vector!

10. Graphical Addition of Vectors: Head to Tail-B
A - B = R R A
A + (-B) = R
R is called the resultant vector!

11. Vectors: Components
Horizontal (x-components) and vertical (y-components) must be added separately to determine the value of Δx and Δy. C
Δx = A + C
Δy = B R B A

12. Vectors: magnitude Can be determined using the following equation:C R B
R = √Δx2 + Δy2 A
Pythagorean Theorem