# RD Sharma Class 12 Chapter 23 Solutions (Algebra Of Vectors)

RD Sharma Class 12 Maths Solutions Chapter 23 Algebra of Vectors are the best study resource for you to prepare for CBSE board exams. In this chapter, you will learn concepts like vector quantities, representation of vectors, types of vectors, parallelogram law of addition of vectors, properties of addition of vectors, subtraction of vectors, multiplication of a vector by a scalar, properties of multiplication of a vector by a scalar etc.

The chapter has a total of 8 exercises and around 80 questions for practice. You can easily solve them with the help of our RD Sharma Solutions and master the chapter. These solutions describe the chapter in detail and reduce the complexity of the problem further. These questions are everything you need to practise to learn the concept to the core. Some other topics of the chapter include position section formulae, a linear combination of vectors, components of a vector in two dimensions, components of a vector in three dimensions, collinearity of points and vectors, coplanarity, direction cosines and direction ratios.

Instasolv provides RD Sharma Solutions for Class 12 Maths Chapter 23 – Algebra of Vectors to you so that you can lay a strong foundation for exams like JEE, NEET and BITSAT. Vector is an important topic for these examinations. Our step by step solutions is the perfect way to clear all your concepts related to the chapter.

## Important Topics in RD Sharma Class 12 Maths Solutions Chapter 23 – Algebra of Vectors

**Defining Vector**

A vector is essentially a physical quantity that represents directions as well as magnitude.

To add a vector there are two methods. Assume the two vectors A and B. To add one vector to the other vector, add the head of the vector to the tail of the other vector.

Let the resultant of the given vectors A and B be C.

Now C = A+B, this addition will be commutative in nature which means

If C= A + B, then C= B+A

The subtraction of two vectors A and B is C = A-B.

**Parallelogram Law of Vector Addition**

The parallelogram law of vector addition holds a considerable similarity with the law of vector addition

The orthogonal system of vector representation, this is the sum of the two vectors

a = a1î+a2ĵ+a3k̂ and

b = b1î+b2ĵ+b3k̂

The components of all the axes are added separately which means

i.e. a + b = aiî+a2ĵ+a3k̂+b1î+b2ĵ+b3k̂

⇒a+b = (a1+b1)î+(a2+b2)ĵ+(a3+b3)k̂

Similar to the addition, the subtraction will be

a-b = (a1–b1)î+(a2–b2)ĵ+(a3–b3)k̂

Now you know how matrices can be added or subtracted.

**Type of Vectors**

**Like and Unlike Vectors**

Two vectors are like vectors when they are pointing in the same direction.

Two vectors are unlike when they are pointing in the opposite directions.

**Unit Vector**

If the modulus of the given vector is unity, then it is a unit vector. The unit vector in the direction the vector b will be known as ‘b cap’.

**Collinear or parallel vectors**

Vectors that have the same support or the vectors with the parallel support are known as the collinear vectors.

**Coterminous of a vector**

Two vectors that have the same terminal point are known as coterminous vectors.

**Discussion of Exercises in RD Sharma Solutions for Class 12 Chapter 23 – Algebra of Vectors**

- Exercise 23.1 has 5 questions where you’ll be asked to represent vectors graphically, classifying vectors and scalars quantities, recognising the type of vector and answering TRUE or FALSE for the given statements.
- Exercise 23.2 comprises 10 questions where you’ll find the vector on the specific condition provided, finding possibilities of other shape formations, etc.
- Exercise 23.3 discusses position vectors of a point, section formulae, linear combination of vectors, etc in 11 questions.
- Exercise 23.4 has 14 questions based on components of a vector in two dimensions, components of a vector in terms of coordinates of its endpoints, etc.
- Exercise 23.5 is based on components of a vector in three dimensions, and performing operations such as addition, subtraction and multiplication of a vector with a scalar and determining equality in component-terms. There are 20 questions in the exercise.
- Exercise 23.6 discusses collinearity and collinearity of points in 7 questions.
- Exercise 23.7 discusses coplanarity in 10 questions.
- Exercise 23.8 has 10 questions based on direction cosines and direction ratios.

### Benefits RD Sharma Solutions for Class 12 Chapter 23 – Algebra of Vectors by Instasolv

- Instasolv provides exercise-wise RD Sharma Class 12 Maths Solutions.
- Instasolv prepares you to appear in CBSE and other exams with confidence and full preparation.
- On practising questions and answers for Chapter 23, you will easily be able to solve the problems that are different from what you have found in NCERT book.