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Vector and Geometry Examples for Specialist Mathematics Week 3

Explore vector products, scalar triple products, and properties in geometry with solutions and exercises. Includes area and volume calculations.

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Vector and Geometry Examples for Specialist Mathematics Week 3

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  1. Specialist Mathematics Vectors and Geometry Week 3

  2. Example 13 (Ex 4F) 8cm B 3cm C 2cm A

  3. Solution 13 8cm B 3cm C 2cm A

  4. Vector Product

  5. Example 14 (Ex 4G1)

  6. Solution 14

  7. Direction of a x b

  8. Length of a x b

  9. Properties of a x b • a x b is a vector perpendicular to both a and b. • a x a = 0 • a x b = - b x a • a x (b + c) = a x b + a x c • (a + b) x (c + d) = a x c + a x d + b x c + b x d

  10. Scalar Triple Product

  11. Example 15 (Ex 4G1)

  12. Solution 15

  13. Example 16 (Ex 4G1)

  14. Solution 16

  15. Example 17 (Ex 4G1)

  16. Solution 17

  17. Area of a Triangle

  18. Area of a Parallelogram

  19. Volume of a Parallelepiped

  20. Volume of a Tetrahedron

  21. Example 18 (Ex 4H)

  22. Solution 18

  23. Example 19 (Ex 4H)

  24. Solution 19

  25. Coplanar Points

  26. Example 20 (Ex 4H)

  27. Solution 20

  28. This weeks work • Text Pages 146 to 156. • Exercise 4F Q 12 – 21 • Exercise 4G1 Q 1 – 14 • Exercise 4G2 Q 2 – 5 • Exercise 4H Q 1 - 10

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