# NCERT Exemplar Class 12 Maths Chapter 10 Solutions: Vector Algebra

NCERT Exemplar Class 12 Maths Solutions Chapter 10 – Vector Algebra includes all the necessary to severe level of understanding of the topics. Whether it be section formula, scalar or vector product, you can practice all the concepts through NCERT Exemplar Class 12 Maths problems and solutions for chapter 10.

Vector algebra is an important topic when you look from the competitive exam’s perspective. This chapter covers various operations on vectors along with many of their geometric properties, algebraic properties, and their applications. There are 45 exemplar questions divided into different exercises. These questions are framed as short-answer type, long-answer type, multiple-choice questions (MCQs), true-false questions, and fill in blanks type questions.

NCERT Class 12 Maths Chapter 10 Exemplar problems and solutions are set up so that you can assemble the essential concepts required to tackle the questions in exams. Our subject matter experts have included all the reasoning and formulae along with the solutions. This will make you prepare for any level of difficulty in the exams.

## Important Topics for NCERT Exemplar Class 12 Maths Solutions Chapter 10 – Vector Algebra

NCERT Exemplar problems class 12 maths chapter 10 solutions mainly focus on properties and applications of vectors. The different topics that are discussed in this chapter are the addition and multiplication of a vector, vector joining two points, and the multiple components of a vector. Towards the end comes topics like section formula, scalar product, and vector product of two vectors. Here are some important points related to NCERT Exemplar Class 12 Maths Chapter 10 ‘vector algebra’ Exemplar problems and solutions:

**Vector:**Any quantity that has magnitude along with the direction. Represented as a^**Vector joining two points:**suppose if we have two points A1(x1,y1,z1) and A2(x2,y2,z2) the resultant vector will be**A1A2 = (x1-x2)i + (y1-y2)j + (z1-z2)k,**where i,j,k represent the three directions of any plane**Section formula:**if any point divides a line segment joining 2 points A and B whose vector is a and b respectively in some ration m:n then there are two cases.

Case 1 – if the division is internal it is given by (**na+mb/m=n**)

Case 2 – if the division is external it is given by (**mb-na/m-n**)

**Scalar product:**The scalar or dot product of any two vectors a and b having some angle θ between them is calculated as –**a.b = |a| |b| cos θ****Vector product:**The vector or cross product of any two vectors a and b having some angle θ between them is defined as-**a × b = |a| |b| sin θ nˆ**

where nˆ is a unit vector perpendicular to the plane containing vectors a and b

### Exercise Discussion of NCERT Exemplar Class 12 Maths Problems and Solutions Chapter 10 – Vector Algebra

- The first 14 NCERT Exemplar questions of class 12 maths chapter 10 are short answer types. They test your necessary skills and formula applications. They are focussed on finding the position and angle between vectors.
- The next four exemplar problems from 15-18 are long answer types, which are based mostly on numerical problems. It will help you practice all the moderate to severe level questions based on similar topics.
- 15 MCQs from 19-33 are asked where you have to choose one option; they are based on numerical problems, You should be very familiar with the basic idea about the formulas of all the concepts used in the chapter.
- From exemplar problems, 34-40 are fill in the blanks problems require one-word answers. It will check your attention skills as the questions will be based on between the lines explanations.
- The next set of exemplar problems from 41-45 includes the true-false questions asking you to tell whether the given statement is incorrect or not. It is used to test your basic mistakes of signs or formulas.

## Why Use NCERT Exemplar Class 12 Maths Solutions Chapter 10 by Instasolv?

- NCERT Exemplar Class 12 Maths Solutions Chapter 10 is a very authentic source of learning. These solutions will lower your burden so that you can concentrate on other chapters too.
- We have provided all the NCERT Exemplar problems and solutions for class 12 maths chapter 10 online at zero cost for you.
- We suggest that you follow these solutions and solve all your doubts regarding vectors and scalar multiplication and the properties of vectors.
- Along with this, we also provide NCERT Exemplar problems and solutions for all chapters of CBSE Class 12 Maths.