**NCERT Solutions for Class 12 Maths Chapter 10: **You can learn about the difference between a scalar and a vector quantity, their properties, vector operations, and more in the NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra. This topic is essential in assisting students in achieving excellent grades not only in the **12th board** exams but also in competitive exams.

**All you need to know about NCERT Solutions Class 12 Maths**

We are here with Vector Algebra Class 12 NCERT Solutions for a subtle yet powerful initiation to sit with your chapter 10 from the Maths curriculum. Hence, Download and go through the Chapter 10 Maths Class 12 Solutions PDF!

Table of Contents

**Download NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra PDF**

It’s crucial to be prepared for the different **Class 12 Maths** problems that will be asked during the 12th board exam. Students gain trust in their ability to write better exams after completing various lessons and problem sets.

**Access Vector Algebra Class 12 NCERT Solutions PDF**

NCERT-Solutions-Class-12-Maths-Chapter-10-Vector-Algebra pdf

These Vector Algebra Class 12 NCERT Solutions are also available for free download, allowing you to practice them offline.

**What will you get in NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra?**

The unit Vectors and Three-Dimensional Geometry includes the chapter Vector Algebra, which accounts for 14 of the total marks. This chapter includes **four exercises** as well as a **miscellaneous exercise** to help students grasp the concepts of vectors and vector algebra. The following are the topics covered in the tenth chapter of NCERT Solutions for Class 12 Maths:

- Vector position
- Direction cousins
- Zero vectors
- Unit vectors
- Coinitial vectors
- Collinear vectors
- Equal vectors
- Negative of a vector
- Properties of vector addition.

**Let us now have a thorough look at the content of the chapter-**

10.1 |
Introduction |

10.2 |
Basic concepts |

10.3 |
Types of vectors |

10.4 |
Addition of vectors |

10.5 |
Multiplication of a vector |

10.5.1 |
Components of a vector |

10.5.2 |
Vector joining two points |

10.5.3 |
Section formula |

10.6 |
Product of Two Vectors |

10.6.1 |
Scalar (or dot) product of two vectors |

10.6.2 |
Projection of a vector on a line |

10.6.3 |
Vector (or cross) product of two vectors |

**Let us now take a quick look at the exercise solution section-**

Exercise Solution 10.1 |
5 Questions |

Exercise Solution 10.2 |
19 Questions |

Exercise Solution 10.3 |
18 Questions |

Exercise Solution 10.4 |
12 Questions |

Miscellaneous Exercise Solution |
19 Questions |

#### Let us now check out the subtopic and exercise solutions that this chapter includes-

**NCERT Solutions for Class 12 Maths Chapter 10: 10.1**

This section introduces us to zero vector, unit vector, and collinear vector. This portion of the chapter talks about definitions of the mentioned terms, with proper examples to make the chapter easy and understandable. The sums which you will basically get to solve and practice from the section centers around differences in vectors which are represented through the graphical presentation.

**NCERT Solutions for Class 12 Maths Chapter 10: 10.2**

This segment of the chapter introduces you to the parallelogram law of vectors. NCERT Solutions for Class 12 Maths Chapter 10 covers every area which will help you learn the techniques to solve the sums. Make sure to practice the same for a concrete grasp on the topic.

**NCERT Solutions for Class 12 Maths Chapter 10: 10.3**

This section works teaching the students about finding the product of two vectors along with the vital process of estimating a vector in line. You will get a hand on the lesson to find out the value of the angle between two vectors.

**NCERT Solutions for Class 12 Maths Chapter 10:10.4**

This portion of the chapter covers the cross-products of vectors and teaches students how to find out the magnitude of the same. To build a clear understanding of the chapter make sure to learn the topic from 12th Class Maths chapter 10 NCERT solutions pdf, at the comfort of your home.

**NCERT Solutions for Class 12 Maths Chapter 10:Miscellaneous**

This is the last section which covers all the questions and subjects corresponding to the topics you read till now. Going through the sums enlisted down in the miscellaneous section enables you to participate in a robust revision session. This is great for you to get ready-made revision papers that will ultimately help you with Maths finals preparation.

**NCERT Solutions for Class 12 Maths Chapter 10: Terms and Definitions**

**Vector:** Those quantities which have magnitude, as well as direction, are called vector quantities or vectors.

- Note: Those quantities which have only magnitude and no direction, are called scalar quantities.

**Representation of Vector**: A directed line segment has magnitude as well as direction, so it is called a vector.

**Magnitude of a Vector:** The length of the vector is called the magnitude of a vector.

**Position vector:** A straight line having one end fixed to a body and the other end attached to a moving point and used to describe the position of the point relative to the body is the position vector. As the point moves, the position vector will change in length or in direction or in both length and direction.

**Direction Cosines:** If α, β and γ are the angles which a directed line segment OP makes with the positive directions of the coordinate axes OX, OY and OZ respectively, then cos α, cos β and cos γ are known as the direction cosines of OP and are generally denoted by the letters l, m and n respectively.

**Types of Vectors~~**

**Null vector or zero vector:** A vector, whose initial and terminal points coincide and magnitude is zero, is called a null vector.

**Unit vector:** A vector of unit length is called a unit vector

**Collinear vectors:** Two or more vectors are said to be collinear if they are parallel to the same line, irrespective of their magnitudes and directions.

**Coinitial vectors:** Two or more vectors having the same initial point are called coinitial vectors.

**Equal vectors:** Two vectors are said to be equal if they have equal magnitudes and the same direction regardless of the position of their initial points.

**Negative vector:** Vector having the same magnitude but opposite in direction of the given vector, is called the negative vector

**Also Access:**

**Also Access:**

**Benefits of NCERT Solutions for Class 12 Maths Chapter 10**

NCERT Solutions for Class 12 Maths Chapter 10 is what you need right now for your chapter 10 exam preparation. So, here we are looking down on some of the proficient advantages which are the reasons for you to go for NCERT Solutions for Class 12 Maths Chapter 10. Let’s begin-

- Assist students with their homework and competitive tests.
- Content is well-structured.
- Assist students in reinforcing their fundamental understanding of vector algebra.
- Subject expertise assisted in the preparation of these NCERT Solutions.

**This is everything that you need for preparing CBSE NCERT Solutions for 12th Maths Chapter 10. We wish you do great in your finals. Also, if you are facing any doubts regarding the same, make sure to comment down so that our professional may reach out to you.**

**FAQs: Vectors Class 12 Maths NCERT Solutions**

### How many questions were there in exercise 10.2 of chapter 10 Maths class 12?

There are a total of 19 questions in exercise 10.2 of chapter 10 Maths class 12.

### Are Class 12 Maths NCERT solutions Ch 10 important to study?

Yes. Chapter 10 Class 12 Maths is an important topic to study for 12th board preparation.

### Can I receive an overview of the Ch 10 Maths Class 12 Solutions exercises?

Yes. You can receive an overview of the Ch 10 Maths Class 12 Solutions exercises from the above blog.

### Can I get a perfect score on the NCERT Solutions for Chapter 10 Maths Class 12?

Yes. KopyKitab’s experts created the NCERT Solutions for Chapter 10 Maths Class 12 after performing extensive research on each term. It will help you to score 100 in Class 12 Maths.

### How many exercises are there in Chapter 10 of the NCERT textbook for Class 12 Maths?

In total, there are 4 exercises in Chapter 10 Class 12 Maths.

### Where can I download Maths Chapter 10 Class 12 NCERT solutions?

You can download NCERT Solutions for Class 12 Maths Chapter 10 from the above blog.

### Are NCERT Solutions for Class 12th Maths Chapter 10 sufficient for board examinations preparation?

Yes. NCERT Solutions for Chapter 10 Class 12 Maths is sufficient for board examinations preparation.