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RD Sharma Class 12 Maths Solutions Chapter 24 - Scalar Or Dot Product

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RD Sharma Solutions for Class 12 Maths Chapter 24 - Scalar Or Dot Product - Free PDF Download

RD Sharma Solutions of Class 12 Maths Chapter 24 Scalar or Dot Product is now available on Vedantu in a PDF format. These RD Sharma Class 12 Scalar Or Dot Product solutions will help students learn the fundamentals of the dot products. To help students grasp the concepts clearly, we are providing RD Sharma Class 12 Chapter 24 step-wise solutions prepared by highly experienced teachers at Vedantu. You can download the RD Sharma Solutions of Class 12 Maths Chapter 24 from Vedantu for free of cost and refer to them for your exam preparation.  Students can download Class 12 RD Sharma Chapter 24 Scalar or Dot Product Solutions at Vedantu’s official website

Competitive Exams after 12th Science

Introduction to The Chapter

Scalar and Vector products are two ways of multiplying 2 vectors. In other words, the dot product is the sum of the multiplication of the corresponding entries scalar and Vector products are two ways of multiplying 2 vectors. In other words, the dot product is the sum of the multiplication of the corresponding entries of 2 sequences of numbers.


Different Types of Vectors

There are different types of vectors based on their magnitude, direction, and their relationship with other vectors:

  • Zero Vectors

Zero Vectors are vectors with 0 magnitudes. 

  • Unit Vectors

Vectors that have a magnitude that is equal to 1 are called unit vectors.

  • Position Vectors

Position vectors are vectors that determine the exact position and direction of movement of the vectors in 3-dimensional spaces. 

  • Equal Vectors

Equal Vectors are those vectors that have their corresponding components equal. Equal vectors will always have the same magnitude and direction. They may have different starting and ending points but the magnitude and direction are always equal.

  • Negative Vectors

A Negative Vector of a vector is negative when it has the same magnitudes but opposite directions. 

  • Parallel Vectors

Parallel Vectors are vectors that have the same direction but not necessarily the same magnitude. 

  • Co-initial Vectors

Co-initial Vectors are the vectors that always have the same initial point.

  • Orthogonal Vectors

Orthogonal Vectors are two vectors when the angle between them is 90 degrees.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 24 - Scalar Or Dot Product

1. What properties does the Dot Product of Vectors have according to Class 12 Chapter 24?

Class 12 students should know all the properties of Dot products of vectors as they come in handy in solving complex numerical problems. The properties of the dot product of vectors

  • Commutative property

  • Distributive property

  • Natural property

  • General properties

  • Vector identities

For some practice on the properties of Dot product of vectors, Class 12 students can solve RD Sharma Chapter 24 which contains a lot of questions on the particular topic. RD Sharma also has solved examples that will help the student to understand the methods of solving questions.

2. What is a projection of a Vector according to Class 12 Chapter 24?

The dot product of vectors is very useful for finding the component of 1 vector in the direction of the other. The vector projection of 1 vector, over another vector, is the exact length of the shadow of the first vector over another vector. The projection of vectors is calculated by getting the product of the magnitude of the given vectors with the cos of the angle between the two vectors. The result of a vector projection formula is always a scalar value. This is called the projection of vectors. 

3. Should I solve RD Sharma for Class 12 Scalar or Dot products?

Class 12 students should definitely solve RD Sharma for Scalar or Dot products as they consist of good-type questions that help the student to understand the fundamentals of scalar or vector products. The topic of Scalar or Dot products is a relatively part of the Chapter Vectors and can be mastered with appropriate practice. Students of Class 12 will benefit greatly from solving RD Sharma for scalar or dot products. They can also refer to Vedantu’s important questions which contain selected and important questions for the best results.

4. What is the Dot Product of 2 Vectors?

Dot Product of 2 Vectors is the multiplication of the magnitudes of 2 vectors, and cos of the angle between the 2 vectors. The dot product of 2 vectors is constructed by taking the component of 1 vector in the direction of the other and taking its product with the magnitude of the other vector. The result of the dot product of 2 vectors always lies in the same plane, of the 2 vectors. The dot product can be both a positive and a negative real number. 

5. How to find the angle between two vectors using dot product?

Dot Product of two vectors is one of the ways of multiplying two or more vectors. The angle between two vectors is obtained as the cos of the angle between the 2 vectors. The cos of the angle between two vectors is always equal to the sum of the product of the individual terms of the two vectors, and the whole divided by the product of the magnitude of the 2 vectors. Thus, the formula for the angle between the two vectors is cosθ=→a.→b|a|.|b|