1. Vectors in Two and Three Dimensions

2. Definition A vector is a quantity that is determined by a magnitude and a direction.

3. Speed vs. Velocity

4. Vector and Scalar Quantities Velocity Displacement Momentum Force Torque Acceleration Speed Distance Voltage Temperature Time Volume Mass

5. Computer Graphics Robot Arms

6. Arrow Representation

7. Cartesian Coordinate Represenatation of a Vector

8. Find the coordinate representation.

9. (3,2)

10. Unit Vectors x y z i j k

11. Unit Vector Representation y x z

12. Vector Addition y x z (2,3,4) (1,-2,2)

13. Vector Addition y x z (2,3,4) (1,-2,2) (3,1,6)

14. Vector Addition y x z (2,3,4) (1,-2,2) (3,1,6)

15. Vector Addition y x z (2,3,4) (1,-2,2) (3,1,6)

16. The Zero Vector and Additive Inverse

17. Properties of Vector Addition

18. Scalar Multiplication x y z

19. Properties of Scalar Multiplication

20. Length of a Vector

21. Example

22. Definition of Unit Vector

23. Example

24. Application

25. Problems Show that the diagonals of a parallelogram bisect each other. Show that the line through the midpoints of adjacent sides of a parallelogram bisect one of the diagonals in the ratio 1:3. Show that the quadrilateral whose vertices are the midpoints of the sides of an arbitrary quadrilateral is a parallelogram.