LHE 11.1 Vectors in the Plane

1. LHE 11.1Vectors in the Plane Calculus III September 10, 2009 Berkley High School

11. Definition of Vectors • A vector is an object having both a magnitude and a direction.

12. Notation • P is at the “tail” or “initial point” • Q is at the “head” or “terminal point” Q P

13. Notation • We will use the notation with the arrow over the vector’s name. • The book uses a bold letter to signify a vector, but it is difficult to do this in your notes. Q P

14. Operations with vectors

15. Vectors in Component Notation • Because vectors can be moved anywhere without changing, a vector, we can think about the vector as the location of the head of the vector when the tail is on the origin. • Although it looks like a coordinate, we use different notation:

16. Vectors in Component Notation

17. Vectors in Component Notation

18. Vectors in Component Notation

20. Definitions • Zero vector: vector with magnitude 0

21. Notation

22. Scalar Multiplication • Scalars are real numbers, not vectors

23. Operations with vectors

25. Unit vectors Unit vectors are vectors with magnitude=1 Any vector (with the exception of the zero vector) can be transformed into a unit vector.

27. Special Unit Vectors

28. Rewriting component form

29. Converting from polar form

32. Vectors on the TI-89 • Use NewProb before starting (in the F6 menu) • [5,2]→u (Square brackets, not parenthesis) • 2u • unitV(u) (Math:Matrix:Vector Ops:UnitV)

33. Assignment • Section 11.1, 1-17 odd, 23-57 odd