1. Meeting 23 Vectors

2. Vectors in 2-Space, 3-Space, and n- Space We will denote vectors in boldface type such as a, b, v, w, and x, and we will denote scalars in lowercase italic type such as a, k, v, w, and x. When we want to indicate that a vector v has initial point A and terminal point B.

3. Vector addition as a process of translating points

5. Vector Subtraction

6. Scalar Multiplication

7. Vectors in Coordinate Systems We will write v = (v 1, v 2 ) to denote a vector v in 2-space with components (v 1, v 2 ), and v = (v 1, v 2, v 3 ) to denote a vector v in 3-space with components (v 1, v 2, v 3 ).

8. Vectors Whose Initial Point Is Not at the Origin

9. n-Space

11. Example

12. The Properties of Vector Operations

13. Norm of a Vector

14. The Properties of a Norm

15. Unit Vectors

16. Example

17. Dot Product

18. Angle between two vectors

19. Component Form of the Dot Product

20. Algebraic Properties of the Dot Product

22. Exercises