# RD Sharma Class 12 Chapter 24 Solutions (Scalar Or Dot Product)

RD Sharma Class 12 Maths Solutions for Chapter 24 Scalar or Dot Product include the methodology behind multiplying or finding the product of the two vectors. The chapter starts with the introduction to vectors and moves to discussing the angle between the two vectors, the scalar or dot product, geometrical interpretation of scalar product, the eight properties of scalar product, scalar product in terms of components, the angle between the two vectors in terms of components, components of a vector along and perpendicular to vector, etc.

This chapter comprises one exercise and 48 questions to test your knowledge and understanding of everything about Scalar or Dot Product. You will be able to practice questions such as two or three vectors are given with a specific magnitude. Consider each vector perpendicular to the sum of the rest, then prove the given statement. The exercise is going to help you learn the complexities involved in the chapter.

Instasolv makes Chapter 24 ‘Scalar or Dot Product’ easier to understand through its solutions. These solutions are provided to you free of cost. You will find all the answers listed in the same arrangement as you find them in RD Sharma Solutions Class 12 Chapter 24. Practice these questions and solutions well to score high marks in your upcoming competitive exams and CBSE exams.

### Topics Discussed in RD Sharma Class 12 Maths Solutions Chapter 24 – Scalar or Dot Product

RD Sharma Class 12 Maths Solutions, for Chapter 24 ‘Scalar or Dot Product’, talk about the notion of multiplication of two vectors. The multiplication of two vectors results in a scalar and a vector. Correspondingly you will get two types of product where one will be a scalar and the other will be a vector.

**The angle between the two vectors**

Let there be two vectors, vector a and vector b. The angle between the two will be the angle formed between their directions when they both converge or they both diverge from the point where the two vectors intersect. Let ø be the angle between vector a and vector b,

then 0 ≤ ø ≤ π

**The scalar product or the Dot product**

Let the vector a and the vector b are two non-zero vectors. These vectors are inclined at ø angle. Then the scalar product of vector a and vector b is given as

Vector a. Vector b

Scalar is |vector a||vector b|cosø

It is evident that the scalar product of the given two vectors will always be a scalar quantity. This is why the product of the two vectors is called the scalar product. As we insert a dot between the two vectors we can also call it a dot product.

It is important to note that if any of the two vectors, vector a or vector b are zero or both are zero, then ø will never be defined as 0 vectors with no direction. In such a scenario, the dot product of the two will be a scalar zero.

**Geometrical Interpretation of Scalar Product**

Let the two vectors a and b are represented by vector OA and Vector OB respectively.

Consider ø, an angle between the two vectors, vector OA and Vector OB.

On Geometrically interpreting, the scalar product of the given two vectors will be the multiplication of either vector and other vector’s projection in the former vector’s direction.

### Discussion of Exercises in RD Sharma Class 12 Maths Solutions Chapter 24 – Scalar or Dot Product

Exercise 24.1 contains 48 questions in total. You will answer questions such as finding the dot product of the given vectors or calculating the value of ∂ in a given equation if the two vectors are perpendicular to each other. You may also answer questions where you will need to find a given equation where the value of two vectors is given if the addition and subtraction of the two vectors along with the value of the second vector are given, then you will need to find the value of the first vector.

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Instasolv has been helping students as you prepare well for CBSE and competitive exams such as JEE Mains and JEE Advanced for years. Maths experts here have years of experience in providing academic help to students in need. Through easy-to-understand RD Sharma Solutions and less complex approaches, it will become very easy for you to acquire the concept and apply it to solve all your ‘Scalar or Dot Product’ problems you get in exams. Instasolv provides you solutions free of cost because education should not come at a price. Our goal is to prepare you for a great start that helps you excel in your career.