Chapter 21: Vectors

21.1: Introduction

1. Scalar and Vector Quantities
2. Problem-Scalar and Vector Quantities
3. Terminologies and Notations of Vectors
4. Equal Vectors
5. Vectors which are Opposite
6. Problem-Vectors which are Opposite
7. Column Vectors
8. Addition of Vectors
9. Problem-Addition of Vectors
10. Vector Addition is Associative
11. Problem-Vector Addition is Associative
12. Zero Vectors
13. Subtraction of Vectors
14. Problem-Subtraction of Vectors
15. Scalar Multiple of a Vector
16. Problem-Scalar Multiple of a Vector
17. Expression of a Given Vector in Terms of two Vectors
18. Problem-Expression of a Given Vector in Terms of two Vectors
19. Position Vectors
20. Problem-Position Vectors
21. Properties of Magnitude of Vector
22. Problem-Properties of Magnitude of Vector
23. More on Notation for Representing Vectors in Plane
24. Problem-Notation for Representing Vectors in Plane
25. Components of a Vector
26. Properties of Vectors in Plane
27. More on Properties of Vectors in Plane
28. A Unit Vector in the Direction of Another Vector
29. Problem-A Unit Vector in the Direction of Another Vector
30. Notation for Vectors in Coordinate System
31. Problem-Notation for Vectors in Coordinate System
32. The Ratio Formula in Vector
33. Problem1-The Ratio Formula in Vector
34. Problem2-The Ratio Formula in Vector
35. Mid-Point Theorem By Vectors
36. Diagonals of Parallelogram Bisect Each Other by Vectors
37. Ratio Theorem By Vectors
38. Problem-Ratio Theorem By Vectors

21.2: Introduction of Vector in Space

1. Introducing Vector Geometry
2. Problem-Introducing Vector Geometry
3. Concept of Vector in Space
4. Problem-Concept of Vector in Space
5. More on Vectors in Space
6. Properties of Vectors
7. Problem-Properties of Vectors
8. Vectors Addition in Space
9. Problem-Vectors Addition in Space
10. Scalar Multiplication in Space
11. Problem-Scalar Multiplication in Space
12. Notation of Vectors in Space
13. Problem-Notation of Vectors in Space
14. Distance Between Two Points in Space
15. Problem-Distance Between Two Points in Space
16. Direction Angles and Direction Cosines of Vector
17. Problem-Direction Angles and Direction Cosines of Vector

21.3: The Scalar Product 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. Problem-Application of Scalar Product on Geometry
20. More on Application of Scalar Product on Geometry

21.4: Cross Product or Vector Product of Two Vectors

1. Cross Product of Two Vectors
2. Problem-Cross Product of Two Vectors
3. Derivation of Useful Results of Cross Product
4. Problem-Derivation of Useful Results of Cross Product
5. Expression of Cross Product in Terms of Components
6. Problem-Expression of Cross Product in Terms of Components
7. Cross Product of Unit Vectors
8. Properties of Cross Product
9. Problem-Properties of Cross Product
10. More on Properties of Cross Product
11. Analytical Expression of Cross Product
12. Direction Numbers or Direction Ratios
13. Problem-Direction Numbers or Direction Ratios
14. Collinear and Coplanar Vectors
15. Problem-Collinear and Coplanar Vectors
16. Vectors Application to Geometry
17. Problem1-Vectors Application to Geometry
18. Problem2-Vectors Application to Geometry
19. Moment of Force
20. Problem-Moment of Force
21. Condition of Parallel Vectors in Cross Product
22. Problem-Condition of Parallel Vectors in Cross Product
23. Area of Parallelogram by Vectors
24. Area of Triangle by Vectors
25. Vector Equation of Line in 3D
26. Problem-Vector Equation of Line in 3D
27. Application of Vector Equation
28. Problem1-Application of Vector Equation
29. Problem2-Application of Vector Equation

21.5: Scalar Triple Product of 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