 Download Download Presentation Vectors and Analytic Geometry in Space

# Vectors and Analytic Geometry in Space

Download Presentation ## Vectors and Analytic Geometry in Space

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. Vectors and Analytic Geometry in Space Dr. Ching I Chen

2. z=constant (0,y,z) (0,0,z) P(x,y,z) (x,0,z) (0,y,0) O (x,0,0) y=constant (x,y,0) x=constant 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(1)Cartesian Coordinates To locate points in space, it uses three mutually perpendicular coordinate axes. The x-, y-, and z-axes shown there make a right-handed coordinate frame.

3. z (0, 0, 5) (2,3,5) line y=3, z = 5 plane z=5 line x=2, z = 5 plane x=2 plane y=3 (0, 3, 0) (2, 0, 0) y x line x=2, y = 3 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(2)Cartesian Coordinates

4. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(3)Cartesian Coordinates To locate points in space, it uses three mutually perpendicular coordinate axes. The x-, y-, and z-axes shown there make a right-handed coordinate frame.

5. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(4, Example 1)Cartesian Coordinates

6. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(5, Example 2)Cartesian Coordinates

7. (0, 0, 1) P(x, y, z) (0, 1, 0) (1, 0, 0) O 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(6)Vector in Spaces

8. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(7)Vector in Spaces

9. O 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(8, Example 3)Vector in Space

10. O 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(9)Magnitude

11. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(10)Zero and Unit Vectors

12. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(11)Magnitude and Direction

13. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(12, Example 4)Magnitude and Direction

14. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(13, Example 5)Magnitude and Direction

15. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(14, Example 6)Magnitude and Direction

16. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(15)Distance and Spheres in Space

17. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(16, Example 7)Distance and Spheres in Space

18. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(17)Distance and Spheres in Space

19. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(18, Example 8)Distance and Spheres in Space

20. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(19, Example 9)Distance and Spheres in Space

21. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(20)Midpoints of Line Segments

22. 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(21, Example 10) Midpoints of Line Segments

23. 11.2 Dot Product (1)Component Form

24. 3 2 11.2 Dot Product (2, Example 1)Component Form

25. 11.2 Dot Product (3)Component Form

26. 11.2 Dot Product (4, Example 2)Component Form

27. 11.2 Dot Product (5)Properties of the dot product

28. 11.2 Dot Product (6, Theorem 1)Perpendicular (Orthogonal) Vectors and Projections

29. 11.2 Dot Product (7, Example 3)Perpendicular (Orthogonal) Vectors and Projections

30. Q B A S P R Q B A S R P 11.2 Dot Product (8)Perpendicular (Orthogonal) Vectors and Projections

31. 11.2 Dot Product (9, Example 4)Perpendicular (Orthogonal) Vectors and Projections

32. 11.2 Dot Product (10, Exploration 1-1)Perpendicular (Orthogonal) Vectors and Projections

33. 11.2 Dot Product (11, Exploration 1-2)Perpendicular (Orthogonal) Vectors and Projections

34. 11.2 Dot Product (12, Exploration 1-3)Perpendicular (Orthogonal) Vectors and Projections

35. 11.2 Dot Product (13, Exploration 1-4)Perpendicular (Orthogonal) Vectors and Projections

36. 11.2 Dot Product (14, Exploration 1-5)Perpendicular (Orthogonal) Vectors and Projections

37. B A 11.2 Dot Product (15)Writing a Vector as a Sum of Orthogonal Vectors

38. 11.2 Dot Product (16, Example 5)Writing a Vector as a Sum of Orthogonal Vectors

39. F D P Q 11.2 Dot Product (17)Work

40. F D P Q 11.2 Dot Product (18, Example 6)Work

41. 11.3 Cross Products (1)Definition of Cross Product

42. 11.3 Cross Products (2)Definition of Cross Product

43. 11.3 Cross Products (3)Are Cross Products Commutative

44. j i k 11.3 Cross Products (4)Are Cross Products Commutative

45. B h= |B||sin q| q A 11.3 Cross Products (5)|AB| Is the area of a parallelogram

46. 11.3 Cross Products (6)Torque

47. 3-ft bar P Q 20-lb magnitude force F 11.3 Cross Products (7, Example 1)Torque

48. 11.3 Cross Products (8)Associative and Distributive Laws

49. 11.3 Cross Products (9)Determinant Formula for A × B