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Vectors and Analytic Geometry in Space

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Vectors and Analytic Geometry in Space

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  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

  50. 11.3 Cross Products (10, Example 2)Determinant Formula for A × B