1. 12 A VECTORS AND SCALARS 12 B GEOMETRIC OPERATIONS HOMEWORK: VIEW POWER POINT BEFORE NEXT CLASS

2. 12A VECTORS AND SCALARS

3. 12A: VECTORS AND SCALARS  Scalars – quantities that only have one magnitude  Examples: speed of a plane  Vectors – quantities that have both magnitude and direction  Examples: velocity of a plane, acceleration, force, displacement, momentum  Represented by a direct line segment or arrow  The length of the arrow represents the size or magnitude of the quantity and the arrowhead shows the direction.

4. EXAMPLE 1

5. VECTOR NOTATION

6. GEOMETRIC NEGATIVE VECTORS

7. GEOMETRIC VECTOR EQUALITY Two vectors are equal if they have the same magnitude and direction. Equal vectors are parallel and in the same direction, and are equal in length. Given a magnitude and direction, vectors can be drawn from any point.

8. EXAMPLE 2

9. 12B GEOMETRIC OPERATIONS WITH VECTORS

10. GEOMETRIC VECTOR ADDITION

11. STEPS FOR CONSTRUCTING VECTOR ADDITION

12. THE ZERO VECTOR

13. EXAMPLE 4

14. GEOMETRIC VECTOR SUBTRACTION To subtract one vector from another, add its negative.

15. EXAMPLE 5

16. EXAMPLE 6

17. VECTOR EQUATIONS Given a closed polygon, you can write a vector equation which relates vectors. There are multiple ways to write equivalent equations.

18. EXAMPLE 8

19. GEOMETRIC SCALAR MULTIPLICATION

20. EXAMPLE 9

21. EXAMPLE 10

22. NEXT CLASS There will be time for questions over these slides. However, you must do your best to follow the material before next class. You will work on homework during class (flipped classroom).