Vectors
This chapter has eight sections. The first chapter contains an introduction to vectors. The basic definition of the vector can be an arrow in the Euclidean plane and vector has both magnitude and direction. An elaborate explanation of nine types of vectors like Zero vectors, Unit vectors, Collinear vectors etc. is provided in this section. The second section deals with Basic vector operations. This section covers addition and subtraction of vectors, multiplication of a vector by a scalar, the basis of a vector space, resolution of a vector in a given basis etc. The third section deals with Dot product. In this section, we will learn how we can define the product of two vectors. In section four, we will learn about another form of vector product “Cross Product” that is extremely useful to discuss different physical phenomena. The section five deals with Scalar triple production. As the name suggests, a scalar triple product involves the (scalar) product of three vectors. We will learn about how such a product be defined in this section. The section six deals with Vector triple product and this is explained extensively with appropriate examples. The section seven deals with the topic “More geometry with vectors”. The vectors approach to geometrical problems is dealt with more deeply in this section. At the end of this section, we have a series of exercises to test your understanding of this chapter, solved examples, previous years’ IIT JEE questions pertaining to this chapter.
In addition to preparing for the JEE mains and advanced exams, Cuemath Founder Manan Khurma's study material is helpful for students who are appearing for CBSE, ICSE and other State board exams.
Basics of Vectors
- Introduction To Vectors
- Addition and Subtraction of Vectors
- Examples on Addition and Subtraction of Vectors
- Scalar Vector Multiplication and Linear Combinations of Vectors
- Basis of A Two Dimensional Plane
- Basis of A Three Dimensional Space
- Resolution of Vectors
- Magnitudes Direction Cosines and Direction Ratios of Vectors
- Examples on Basics of Vectors Set 1
- Examples on Basics of Vectors Set 2
- Examples on Basics of Vectors Set 3
- Examples on Basics of Vectors Set 4
- Examples on Basics of Vectors Set 5
Vector Dot and Cross Products
- Vector Dot Product
- Properties of Vector Dot Product
- Examples on Vector Dot Product Set 1
- Examples on Vector Dot Product Set 2
- Examples on Vector Dot Product Set 3
- Vector Cross Product
- Properties of Vector Cross Product
- Examples on Vector Cross Product Set 1
- Examples on Vector Cross Product Set 2
Scalar and Vector Triple Products
- Scalar Triple Product of Vectors
- Properties of Scalar Triple Product of Vectors
- Examples on Scalar Triple Product of Vectors Set 1
- Examples on Scalar Triple Product of Vectors Set 2
- Vector Triple Product of Vectors
- Examples on Vector Triple Product of Vectors Set 1
- Examples on Vector Triple Product of Vectors Set 2
Geometrical Analysis With Vectors
- Examples on Vectors Applied To Tetrahedrons Set 1
- Examples on Vectors Applied To Tetrahedrons Set 2
- Vector Equations of Lines
- Examples on Vector Equations of Lines Set 1
- Examples on Vector Equations of Lines Set 2
- Examples on Vector Equations of Lines Set 3
- Vector Equations of Planes
- Examples on Vector Equations of Planes Set 1
- Examples on Vector Equations of Planes Set 2
Vectors