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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 Page 106 Exercise 5A

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

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

8. Scalar Triple Product Def. Scalar Triple Product

9. Scalar Triple Product ? The Volume of a Parallelopiped

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

11. Scalar Triple Product Ex Page 113 Exercise 5C

12. 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

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

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

15. Equation of a Plane Idea A O

16. Equation of a Plane Idea A R O

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

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

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

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