RS Aggarwal Class 12 Vectors and Their Properties PDF

RS Aggarwal Class 12 Vectors and Their Properties PDF

Welcome to sidclasses.in. Here we have provided RS Aggarwal Class 12 Vectors and Their Properties PDF which you can download very easily. Rs Aggarwal is a mathematics book based on NCERT with lots of questions to practice. If you have cleared your concept from NCERT maths book class 12 then now it’s time for you to go for the question of RS Aggarwal Class 12 Vectors and Their Properties PDF.

What are Vectors and Their Properties?

In mathematics, a vector is an element of a vector space, which is a collection of objects that can be added together and multiplied (“scaled”) by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field.

Vectors are often represented by an ordered list of numbers, called coordinates. For example, in two-dimensional space, a vector can be represented by an ordered pair of numbers (x, y). In three-dimensional space, a vector can be represented by an ordered triple of numbers (x, y, z).

The properties of vectors include:

  • Addition: Two vectors can be added together component-wise, resulting in a new vector. For example, (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2)
  • Subtraction: Two vectors can be subtracted component-wise, resulting in a new vector. For example, (x1, y1) – (x2, y2) = (x1 – x2, y1 – y2)
  • Scalar multiplication: A vector can be multiplied by a scalar, resulting in a new vector. For example, k(x, y) = (kx, ky)
  • Dot product: Two vectors can be multiplied using the dot product, which is a scalar value. The dot product of vectors A and B is A.B = |A| |B| cos(theta)
  • Cross Product: Two vectors can be multiplied using the cross product, which results in a vector that is perpendicular to both A and B. The cross product of vectors A and B is A x B = |A| |B| sin(theta)
  • The magnitude of a vector is the distance of the vector from the origin of the vector space. The magnitude of a vector A = |A|
  • The unit vector is a vector of magnitude 1.
  • A zero vector is a vector that has a magnitude of zero, and it is represented by (0,0,0)

Vectors have wide applications in various fields of physics and engineering as well as in computer science.

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Rs Aggarwal Class 12 PDF (All Chapters PDF)

Chapter no.chapter namepdf
1RelationsDownload
2FunctionsDownload
3Binary OperationsDownload
4Inverse Trigonometric FunctionsDownload
5MatricesDownload
6DeterminantsDownload
7Adjoint and Inverse Of MatrixDownload
8System of Linear EquationsDownload
9Continuity and DifferentiabilityDownload
10DifferentiationsDownload
11Applications of DerivativesDownload
12Indefinite IntegralsDownload
13Methods of integrationDownload
14Some Special integralsDownload
15Integration using Partial FunctionsDownload
16Definite integralsDownload
17Area of Bounded RegionsDownload
18Differential equations and their formationsDownload
19Differential equations with variable separableDownload
20Homogeneous Integral equationsDownload
21Linear Differential equationsDownload
22Vectors And Their PropertiesDownload
23Scalar, or Dot product of VectorsDownload
24Cross or vector products of VectorDownload
25Product of three vectorsDownload
26Fundamental Concepts of 3D GeometryDownload
27Straight Line in SpaceDownload
28The PlaneDownload
29ProbabilityDownload
30Bayes’s Theorem and its ApplicationsDownload
31Probability DistributionDownload
32Binomial DistributionsDownload
33Linear ProgrammingDownload

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