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Vectors PowerPoint Presentation

Vectors

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Vectors

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  1. a a b Vectors C4 Scalar Product The scalar (or dot) product is a way of combining two vectors that results in a useful scalar value.

  2. a a b ? ? Vector Product Def. Vector Product The vector (or cross) product is a way of combining two vectors that results in a useful vector. Right-hand rule. Screwdriver undoing a screw.

  3. Vector Product There was an easy alternate way to find the scalar product, found by considering unit vectors. There must be an easy way to find the cross product too. Idea

  4. Ex ? Vector Product Def. Vector Product (determinant form)

  5. Vector Product Ex

  6. Vector Product Ex Page 106 Exercise 5A

  7. C A A Res. B B O O Applications of Vector Products ?

  8. Applications of Vector Products Ex

  9. Applications of Vector Products Ex

  10. Applications of Vector Products Ex

  11. Applications of Vector Products Ex

  12. Applications of Vector Products Ex Page 110 Exercise 5B

  13. Scalar Triple Product Def. Scalar Triple Product

  14. Scalar Triple Product Ex

  15. Scalar Triple Product ? The Volume of a Parallelopiped

  16. Scalar Triple Product ? What is the volume of this tetrahedron?

  17. Scalar Triple Product Ex

  18. Scalar Triple Product Ex Page 113 Exercise 5C

  19. b r a Vector Equation of a Line C4 A line goes through point A and is parallel to a vector b • To get to any point on the line from the origin • Move from O to A • Move along the line some distance b R A O

  20. R b A r a O Def. Cross Product Equation of a Line Cross Product Equation of a Line Idea

  21. Cross Product Equation of a Line Ex

  22. Def. Cartesian Equation of a (3D) Line Cartesian Equation of a Line Idea Page 113 Exercise 5D

  23. Equation of a Plane Idea A O

  24. Equation of a Plane Idea A R O

  25. Equation of a Plane Ex

  26. Def. Cartesian Equation of a Plane Cartesian Equation of Plane Idea

  27. Equation of a Plane Ex

  28. Equation of a Plane Ex

  29. Equation of a Plane Ex Page 120 Exercise 5E

  30. Equation of a Plane Ex

  31. Equation of a Plane Ex

  32. Equation of a Plane Ex

  33. Equation of a Plane Ex

  34. Equation of a Plane Ex

  35. Equation of a Plane Ex

  36. Equation of a Plane ?

  37. Equation of a Plane Ex

  38. Equation of a Plane Ex

  39. Equation of a Plane Ex

  40. Equation of a Plane Ex

  41. Equation of a Plane Ex

  42. Equation of a Plane Ex Page 128 Exercise 5F

  43. Labels M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise