5. Vectors

Sections

Navigate through the learning materials and practice exercises.

1. 5

   Vectors

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   Vectors are quantities defined by both magnitude and direction, critical in...

2. 5.1

   Introduction To Vectors

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   Vectors are quantities defined by both magnitude and direction, fundamental...

3. 5.2

   Definition Of A Vector

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   A vector is a quantity characterized by both magnitude and direction, which...

4. 5.3

   Types Of Vectors

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   This section covers the various types of vectors, each defined by their...

5. 5.3.1

   Zero Vector

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   The zero vector is a fundamental concept in vector mathematics, defined as a...

6. 5.3.2

   Unit Vector

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   Unit vectors are vectors with a magnitude of one, used to represent...

7. 5.3.3

   Equal Vectors

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   Equal vectors are defined as vectors that have the same magnitude and direction.

8. 5.3.4

   Negative Vector

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   A negative vector has the same magnitude as a given vector but points in the...

9. 5.3.5

   Co-Initial Vectors

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   Co-initial vectors are vectors that share the same starting point but may...

10. 5.3.6

    Collinear Vectors

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    Collinear vectors are vectors that lie along the same straight line,...

11. 5.3.7

    Coplanar Vectors

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    Coplanar vectors are those that lie within the same geometric plane, playing...

12. 5.4

    Representation Of Vectors

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    This section explores how vectors are represented geometrically and...

13. 5.4.1

    Geometric Representation

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    Geometric representation of vectors involves illustrating vectors as arrows...

14. 5.4.2

    Algebraic Representation

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    This section introduces algebraic representation of vectors, explaining how...

15. 5.4.2.1

    In 2d

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    This section introduces the representation and operations of vectors in a 2D...

16. 5.4.2.2

    In 3d

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    This section focuses on the representation and operations of vectors in...

17. 5.5

    Operations On Vectors

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    This section discusses various operations on vectors, including addition,...

18. 5.5.1

    Addition Of Vectors

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    This section explores the fundamental concepts of vector addition, both...

19. 5.5.1.1

    Graphical Method

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    The graphical method of vectors involves adding vectors using a geometric...

20. 5.5.1.2

    Algebraic Method

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    The Algebraic Method section explains how to perform operations on vectors...

21. 5.5.2

    Subtraction Of Vectors

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    This section explains the concept of vector subtraction, illustrating how to...

22. 5.5.3

    Scalar Multiplication

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    Scalar multiplication involves multiplying a vector by a scalar, affecting...

23. 5.5.4

    Dot Product (Scalar Product)

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    The dot product, also known as the scalar product, is a mathematical...

24. 5.5.5

    Cross Product (Vector Product)

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    The cross product of two vectors results in a vector that is perpendicular...

25. 5.6

    Applications Of Vectors

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    This section discusses the various real-world applications of vectors across...

26. 5.7

    Summary Of Chapter 5: Vectors

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    This section summarizes the fundamental concepts and operations of vectors,...