1. Mathematics

2. Session Vectors -2

3. Session Objectives  Vector (or Cross) Product  Geometrical Representation  Properties of Vector Product  Vector Product in Terms of Components  Applications: Vector Moment of a Force about a Point, about a Line  Class Exercise

4. Vector (or Cross) Product O

5. Note

6. Geometrical Representation

7. Properties of Vector Product 1. Vector product is not commutative 2. Vector product is distributive over vector addition

8. Properties of Vector Product Cont.

10. Vector Product in Terms of Components

11. Vectors Normal to the Plane of Two Given Vectors

12. Lagrange’s Identity

13. Example –1 Find a unit vector perpendicular to the plane containing the vectors.

14. Solution Cont.

15. Example –2 Solution: The vector perpendicular to the plane ABC is.

16. Example –3

17. Solution Cont.

18. Example –4

19. Solution Cont.

20. Example –5

21. Solution Cont.

22. Applications

23. Example -6 Find the area of a parallelogram determined by the vectors

24. Solution Cont.

25. Example -7 Find the area of the triangle formed by the points A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).

26. Solution Cont.

27. Moment of Force About a Point O P

28. Example -8

29. Solution Cont. The moment of the force acting through B about the point A is given by

30. Moment of Force About a Line

31. Example -9

32. Solution Cont. The moment of the force about the given line is

33. Geometrical Problem Example -10 In a triangle ABC, prove by vector method that: Solution: By triangle law of vector addition

34. Solution Cont.

35. From (i) and (ii), we get

36. Thank you