# RS Aggarwal Class 12 Chapter 23 Solutions (Scalar or Dot Product of Vectors)

RS Aggarwal Solutions for Class 12 Chapter 23 ‘Scalar or Dot Product of Vectors’ will help you in acing all the competitive exams such as NEET, JEE or BITSAT besides assisting you to get excellent marks in board exams. In the exercises of this chapter, you will learn how to multiply two vectors to get its scalar product. You will also learn how to find the projection of one vector over another vector which is given by the product of the magnitude of the first vector and the cosine of the angle between the two vectors.

There are 34 questions in the exercise of this chapter. The questions are of diverse variety ranging from objective type questions to the questions that require detailed subjective answers with adequate reasoning. You will be able to give finishing touches to your preparation by using this source of a reference as an add on to your course textbook. The questions in RS Aggarwal Solutions for Class 12 Chapter 23 ‘Dot Product of two Vectors’ are samples of the type of questions that you will encounter in your school exam which is why we advise you to study these solutions thoroughly.

The team of maths experts at Instasolv have prepared these solutions keeping in mind the theory that ‘sophistication lies in simplicity’ and hence, you will find these solutions very much in coordination with your level of understanding. The topics and major highlights of chapter 23 are discussed in detail below.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 23- Scalar or Dot Product of Vectors

**Introduction to Dot Product of Vectors**

You have already studied in your previous classes that multiplication of the vectors can be done by employing two popular methods, mentioned as follows:

- Scalar or dot product of two vectors
- Vector or cross product of two vectors.

We will cover the first method in this chapter. Therefore, the product of the magnitude of the given two vectors with the cosine of the angle between them is known as the Dot Product of Vectors. When we use the dot product method to evaluate the product of two given vectors, then we get a scalar quantity.

Therefore, a scalar product of **a **and **b** can be represented mathematically as,

**a.b = |a|.|b|** *cosθ*

Such that |**a**| and |**b**| give the magnitude of the two given vectors and is the angle between two given vectors.

**Projection of Vectors**

When there are two vectors **a **and **b**, and we have to find the projection of vector **a **over **b, **then it is given as |**a**| *cosθ *and in the manner, the projection of vector **b** over **a** is given as |**b**| *cosθ*

Mathematically, it can be expressed as follows,

- Projection of
**a**over**b**:

- Similarly, projection of
**b**over**a**:

**Properties of Dot Product of Two Vectors:**

- Dot Product of given two vectors exhibit commutative property such that
**a.b= b.a = α**.b*cosθ* - When the dot product
**a.b**= 0, then the - Also for two vectors
**a**and**b**, the following property holds true:(d.α).(e.b)=(d.b).(e.α)=de α.b - The dot product of the vector
**a**with itself is equal to the square of its magnitude such that α.α=α^{2} - Dot Product of vectors also exhibit the distributive property that is
**α****.(b + c) = α.b + α.c** - If vector
**a**is given asand

### Exercise Discussion of RS Aggarwal Solutions for Class 12 Chapter 23 – Scalar or Dot Product of Vectors

- The exercise solutions of this chapter will need you to find the dot products in the initial simpler questions.
- You will also learn the relationship between angles and the dot product of the vectors by practising these exercise solutions.
- Some important questions in the exercise include finding angles between vectors, expressing a vector is perpendicular to another vector, finding the vector when their dot product is given, proving that one vector is equal to another.

### Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 23 by Instasolv

The maths experts of Instasolv have broken each solution into simple steps to make it easy and less time consuming for you to understand. You can get the RS Aggarwal Class 12 Maths Solutions absolutely free without any hurdles. We, at Instasolv, keep ourselves updated with the latest trends of exam patterns and guidelines by the board. Therefore, our solutions are reliable.