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Chapter 9: Vectors (100 videos)

9.1: Cartesian Coordinate System for 3D Space
1. Introducing Vector Geometry
2. Problem-Introducing Vector Geometry
3. Concept of Vector in Space
4. More on Vectors in Space
5. Problem-Concept of Vector in Space
 
9.2: Scalar and Vectors Quantities
1. Scalar and Vector Quantities
2. Problem-Scalar and Vector Quantities
3. Terminologies and Notations of Vectors
 
9.3: Equal Vectors
1. Equal Vectors
 
9.4: Position Vector and its Direction Cosines
1. Position Vectors
2. Problem-Position Vectors
3. Direction Angles and Direction Cosines of Vector
4. Problem-Direction Angles and Direction Cosines of Vector
 
9.5: Multiplication of a Vector by a Scalar
1. Scalar Multiple of a Vector
2. Problem-Scalar Multiple of a Vector
 
9.6: Vector Addition
1. Addition of Vectors
2. Problem-Addition of Vectors
3. Vector Addition is Associative
4. Problem-Vector Addition is Associative
5. Zero Vectors
6. Subtraction of Vectors
7. Problem-Subtraction of Vectors
 
9.7: Components of a Vector in a Plane
1. Components of a Vector
2. Properties of Vectors in Plane
3. More on Properties of Vectors in Plane
4. A Unit Vector in the Direction of Another Vector
5. Problem-A Unit Vector in the Direction of Another Vector
6. Notation for Vectors in Coordinate System
7. Problem-Notation for Vectors in Coordinate System
 
9.8: Application to Analytic Geometry
1. Problem-Moment of Force
2. Vectors Application to Geometry
3. Problem1-Vectors Application to Geometry
4. Problem2-Vectors Application to Geometry
5. Moment of Force
 
9.9: The Scalar and Vector Products of Two Vectors
1. Scalar Product of Two Vectors
2. Problem-Scalar Product of Two Vectors
3. Properties of Scalar Product
4. More on Properties of Scalar Product
5. Problem-Properties of Scalar Product
6. Perpendicular Vectors
7. Problem-Perpendicular Vectors
8. Parallel Vectors
9. Problem-Parallel Vectors
10. Scalar Product of Vectors in Their Component Form
11. Problem-Scalar Product of Vectors in Their Component Form
12. Angle Between Two Vectors
13. Problem-Angle Between Two Vectors
14. Projection of One Vector Upon Another Vector
15. Problem-Projection of One Vector Upon Another Vector
16. Application of Scalar Product
17. Problem-Application of Scalar Product
18. Application of Scalar Product on Geometry
19. More on Application of Scalar Product on Geometry
20. Problem-Application of Scalar Product on Geometry
21. Cross Product of Two Vectors
22. Problem-Cross Product of Two Vectors
23. Derivation of Useful Results of Cross Product
24. Problem-Derivation of Useful Results of Cross Product
25. Expression of Cross Product in Terms of Components
26. Problem-Expression of Cross Product in Terms of Components
27. Cross Product of Unit Vectors
28. Properties of Cross Product
29. Problem-Properties of Cross Product
30. More on Properties of Cross Product
31. Analytical Expression of Cross Product
32. Direction Numbers or Direction Ratios
33. Collinear and Coplanar Vectors
34. Problem-Direction Numbers or Direction Ratios
35. Problem-Collinear and Coplanar Vectors
36. Vectors Application to Geometry
37. Problem1-Vectors Application to Geometry
38. Problem2-Vectors Application to Geometry
39. Moment of Force
40. Problem-Moment of Force
41. Condition of Parallel Vectors in Cross Product
42. Problem-Condition of Parallel Vectors in Cross Product
43. Area of Parallelogram by Vectors
44. Area of Triangle by Vectors
45. Vector Equation of Line in 3D
46. Problem-Vector Equation of Line in 3D
47. Application of Vector Equation
48. Problem1-Application of Vector Equation
49. Problem2-Application of Vector Equation
 
9.10: Scalar Products of Three Vectors
1. Scalar Triple Product
2. Problem-Scalar Triple Product
3. Vector Triple Product
4. More on Vector Triple Product
5. Analytical Expression of Triple Product
6. Problem-Analytical Expression of Triple Product
7. Volume of Parallelepiped by Triple Product
8. Problem-Volume of Parallelepiped by Triple Product
9. Volume of Tetrahedron by Triple Product
10. Problem-Volume of Tetrahedron by Triple Product
11. Properties of Triple Scalar Product
12. Problem-Properties of Scalar Triple Product
 
9.11: Applications of Vectors to Mechanics
1. Area of Parallelogram by Vectors
2. Area of Triangle by Vectors
3. Application of Vector Equation
4. Problem1-Application of Vector Equation
5. Problem2-Application of Vector Equation
 

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