Vectors

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Chapter 9: Vectors (88 videos)   (Practice Test)
9.1: Scalar and Vectors Quantities  (Practice Test)
  1. Scalar and Vector Quantities
  2. Problem-Scalar and Vector Quantities
  3. Terminologies and Notations of Vectors
9.2: Equal Vectors
  1. Equal Vectors
9.3: Position Vector and its Direction Cosines  (Practice Test)
  1. Position Vectors
  2. Problem-Position Vectors
  3. Direction Angles and Direction Cosines of Vector
  4. Problem-Direction Angles and Direction Cosines of Vector
9.4: Multiplication of a Vector by a Scalar
  1. Scalar Multiple of a Vector
  2. Problem-Scalar Multiple of a Vector
9.5: Vector Addition  (Practice Test)
  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
9.6: Components of a Vector in a Plane  (Practice Test)
  1. More on Notation for Representing Vectors in Plane
  2. Problem-Notation for Representing Vectors in Plane
  3. Components of a Vector
9.7: Application to Analytic Geometry  (Practice Test)
  1. The Ratio Formula in Vector
  2. Problem1-The Ratio Formula in Vector
  3. Problem2-The Ratio Formula in Vector
  4. Mid-Point Theorem By Vectors
  5. Diagonals of Parallelogram Bisect Each Other by Vectors
  6. Ratio Theorem By Vectors
  7. Problem-Ratio Theorem By Vectors
9.8: The Scalar and Vector Products of Two Vectors  (Practice Test)
  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. Problem-Application of Scalar Product on Geometry
  20. More on 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. Problem-Direction Numbers or Direction Ratios
  34. Collinear and Coplanar Vectors
  35. Problem-Collinear and Coplanar Vectors
  36. Vectors Application to Geometry
  37. Problem1-Vectors Application to Geometry
  38. Problem2-Vectors Application to Geometry
  39. Condition of Parallel Vectors in Cross Product
  40. Problem-Condition of Parallel Vectors in Cross Product
  41. Area of Parallelogram by Vectors
  42. Area of Triangle by Vectors
  43. Vector Equation of Line in 3D
  44. Problem-Vector Equation of Line in 3D
  45. Application of Vector Equation
  46. Problem1-Application of Vector Equation
  47. Problem2-Application of Vector Equation
9.9: Scalar Products of Three Vectors  (Practice Test)
  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
9.10: Applications of Vectors to Mechanics
  1. Moment of Force
  2. Problem-Moment of Force