RD Sharma Class 12 Solutions Chapter 23 - Algebra of Vectors (Ex 23.2) Exercise 23.2

About RD Sharma Class 12

RD Sharma is an author of several textbooks who is a well-known mathematician and an educator. RD Sharma's books are very popular among students of the CBSE board. It is considered to be one of the best and important books in mathematics for classes 9 to 12. This book is a complete package that includes a complete syllabus and relevant questions to practice from. There are a lot of maths topics covered in this book, some of them are, quadratic equations, coordinate geometry, heights and distances, triangles, circles, trigonometric ratios, trigonometric identities, probability, pairs of linear equations in two variables, surface, area and volumes, arithmetic progressions and many more. 

Importance of The Book

• RD Sharma is considered to be a very important book for class 12 because of the wide variety of questions given in the book, which covers all the types of questions that are asked in the board examinations. This helps students to study in a more exam-oriented way which helps them in scoring better marks. The concepts are explained in a simple way with the help of solved questions, which allows even weaker students to understand the concepts easily. 

• It has almost all the questions given in NCERT books and a lot more of its own. This allows students to focus only on one book rather than taking up several books. Students can definitely score much better marks by studying from this single book which has a lot of things in itself. RD Sharma book also gives a strong base or foundation in the mathematics subject. So, the students can have full knowledge in the mathematical field from this book also. 

All You Need to Know About Chapter - Algebra of Vectors

Definition - A vector is a geometric object with both length and direction (and so is also very commonly represented as a ray). The representation of a vector is also similar to its definition. We need two symbols to represent a vector, each used to denote different parameters. One is used to define the length and the other is used to define direction. Vectors can be added, subtracted or multiplied to each other using vector algebra.

Vector Algebra Operations - Just like in usual Algebra, vectors can also be added, subtracted or multiplied to each other using vector algebra. But, in the case of multiplication, there are two different ways in which vectors can be multiplied, which are dot product and cross product.

Addition of Vectors - Let us consider there are two vectors A and B, then the sum of these two vectors can be done when the tail of vector B meets with the head of vector A. Through the course of this addition, the magnitude and direction of the vectors should not change. The vector addition obeys two important laws, which are, Commutative law and Associative law.

Subtraction of Vectors - In subtraction of vectors the direction of the vector which has a negative sign is reversed and then the addition is performed on both the given vectors. If A and B are the vectors, for which the subtraction method has to be performed, then we invert the direction of another vector, say for B, make it -B. Now, we need to add vectors A and -B.