# RS Aggarwal Class 12 Chapter 22 Solutions (Vectors and Their Properties)

RS Aggarwal Solutions for Class 12 Chapter 22 ‘Vector and Their Properties’ have been compiled to guide you in solving the exercise problems in this chapter. Vector is a quantity that we encounter in various sciences and topics of maths, which makes it a crucial topic. Also, this chapter has a significant weightage in the CBSE exams. You will be introduced to vectors in detail and the properties of vectors will assist you in building a strong foundation for the chapters ahead. You will also get to understand the difference between the unit vector and vector by solving these exercise questions.

There are a total of 24 questions in 1 exercise in this chapter. The exercise questions of RS Aggarwal Solutions for Class 12 Chapter 22 Vectors and their properties will increase your proficiency in finding the magnitude of a vector, and identifying its components. The questions are arranged in an order of increasing difficulty level so that you feel compatible with the topics while solving the solutions. This is a very important chapter to build a strong foundation of vectors which will provide you with immense support in pursuing the career of your dreams.

We, at Instasolv, have made sure that you do not leave our platform with any kind of confusion. Therefore, you will find the solutions provided by our experts very simple and detailed with reasons mentioned for each important step. By relying on Instasolv, you will be able to grasp the process of approaching a question of vectors without any complexities. The Instasolv experts are committed to providing you with an effective online source of reference so that you can make the most of your self-study hours.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 22 Vectors and Their Properties

**Introduction to Vectors:**

If an object or value exhibits both magnitudes as well as direction, it is termed as a Vector. Any given vector can be identified by a line with an arrowhead. In such a line denoting a vector, the length is given by the magnitude of the vector and the direction is denoted by the arrowhead. In a case when the direction and magnitude of two given vectors are equal, we may designate the two vectors as equal. The other names of the vector are Euclidean vector, Geometric Vector, and Spatial vector

In Maths, a line representing a vector gives its magnitude through its length and the angle made by it with a given reference is known as the direction component of the vector. The starting point of a given vector is termed as tail while the endpoint which is denoted by the arrowhead is known as the head of the vector.

The vector is used in the simplification of three-dimensional geometry to decipher the complex topics in it. Hence, we may conclude that a vector that has n number of dimensions is an ordered collection of n elements which are termed as the components.

**The magnitude of a Vector**

In the above example, the distance between the two points A and B respectively give the magnitude of the given vector. The Magnitude of the vector would be denoted as

|AB| or |a|

The point that should be kept in mind is that length is never negative which would mean that the magnitude of any vector is always greater than or equal to 0.

**Key Highlight**

- If there is a point A (x, y, z) in free space with respect to the origin O with (0, 0, 0) coordinates. Then, the position vector with respect to the origin of A is written as

→

OA where O would be the tail point and A is the head of the vector.

The magnitude of this vector will be given as

→

- The angles made by this vector with respect to x, y, and z axes respectively are given as α,β,y And their cosines are denoted as l=cosα, m=cosβ, and n=cosy.

**Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 22 – Vectors and Their Properties**

- The exercise questions of RS Aggarwal Class 12 Maths Solutions for Chapter 22 provide comprehensive coverage of all the topics in this chapter.
- The syllabus of the chapter is covered in a detailed manner adhering strictly to the guidelines of the Central Board of Secondary Education.
- The 24 questions will help you build a strong aptitude for understanding the complicated topics from your physics syllabus as well.
- In the exercise, you are required to solve questions like finding the magnitude of vectors, finding unit vectors, finding the position of vectors, finding the direction ratios of the vectors etc.

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The goal of maths experts at Instasolv is to bust the myth that maths is a difficult and boring subject. We, at Instasolv, will help you identify your weak points and work on them consistently to overcome them. Our RS Aggarwal solutions are organized in a systematic way to help you understand each topic step by step.