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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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