# NCERT Solutions Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry goes through the fundamentals of geometry in three dimensions. Students must be familiar by now with the basics of coordinate geometry, such as in order to locate any point in space, we need two intersecting lines, also called coordinate axes, and the information about the two numbers known as the coordinates of the point with respect to the axes. But, what if we want to find the position of an object in real life, then three-dimensional geometry comes into play and we need a third reference. This chapter will introduce geometry in three dimensions where we will require a third factor, i.e., the height of the object from the ground. Thus, these NCERT solutions Class 11 maths Chapter 12 explain the coordinate axes and the coordinate planes in three-dimensional space.

With relevant practical examples, the students will be able to grasp geometrical forms and patterns by combining the power of algebra with coordinate geometry. They will get to learn the practical utility of the three coordinates, and how this can be used to find out measures like point distance and angle between lines, which are the foundation for understanding shapes like triangles and parallelograms. The Class 11 maths NCERT solutions Chapter 12 Introduction To Three Dimensional Geometry pdf files are given below for reference and also download the exercise-wise solutions provided in the links below.

- NCERT Solutions Class 11 Maths Chapter 12 Ex 12.1
- NCERT Solutions Class 11 Maths Chapter 12 Ex 12.2
- NCERT Solutions Class 11 Maths Chapter 12 Ex 12.3
- NCERT Solutions Class 11 Maths Chapter 12 Miscellaneous Exercise

## NCERT Solutions for Class 11 Maths Chapter 12 PDF

The subject of geometry cannot be ignored because it's all around us. One of the most renowned applications of three-dimensional geometry is in the Space-Time Continuum of Einstein’s Theory of Relativity. In order to solve any problem involving a specific shape, it is critical to understand how to measure its dimensions or recognize it. And this is outlined elaborate in the NCERT solutions class 11 maths, which can be downloaded from the links given below :

**ā** Download Class 11 Maths NCERT Solutions Chapter 12

**NCERT Class 11 Maths Chapter 12 **

### NCERT Solutions for Class 11 Maths Chapter 12 Introduction to 3-D Geometry

The branch of mathematics that deals with spatial interactions is known as geometry. It also assists us in finding distances and heights in our everyday lives. From evaluating the capacity of a box to determining the size of a room, the use of three-dimensional geometry is inevitable. As a result, it is critical for the students to understand the concepts of three-dimensional space. An exercise-wise detailed analysis of NCERT Solutions Class 11 Maths Chapter 12 Introduction To Three Dimensional Geometry is given below :

- Class 11 Maths Chapter 12 Ex 12.1 - 4 Questions
- Class 11 Maths Chapter 12 Ex 12.2 - 5 Questions
- Class 11 Maths Chapter 12 Ex 12.3 - 5 Questions
- Class 11 Maths Chapter 12 Miscellaneous Exercise

ā Download NCERT Books for Class 11 Maths Chapter 12

**Topics Covered:** The Class 11 maths NCERT solutions Chapter 12 covers the topics like how coordinates of a point in space are identified, how the distance between two points is calculated, the section formula, and how to prove the collinearity of points using the section formula.

**Total Questions:** The Class 11 Maths Chapter 12 Introduction To Three Dimensional Geometry Chapter 12 consists of 14 questions of which 9 are easy, 3 are moderately simple and 3 are long answer-type questions.

## List of Formulas in NCERT Solutions Class 11 Maths Chapter 12

NCERT solutions Class 11 maths Chapter 12 explains the three-dimensional space in the cartesian coordinate system using the x, y, and z axes. The position of any point in space can be determined using these coordinates. It also presents us with a lot more information when combined with other factors by using certain formulas. This chapter requires the extensive use of formulas. In the absence of these formulas determining, say, the centroid of a triangle, would take days rather than mere minutes. Thus, they form an important component of the NCERT solutions for Class 11 Maths Chapter 12. A few of them are given below:

**Distance between any two points A( x**_{1 }, y_{1 }, z_{1}) and B( x_{2 }, y_{2 }, z_{2}):**√[****(x**_{2}- x_{1 })^{2}+ (y_{2}- y_{1})^{2}+ (z_{2}- z_{1})^{2}]**The coordinates of the mid-point of the line segment which joins two points A( x**_{1 }, y_{1 }, z_{1}) and B( x_{2 }, y_{2 }, z_{2}) are [ (x_{1}+ x_{2})/2, (y_{1}+ y_{2}/2) , (z_{1}+ z_{2}/2) ]**The coordinates of the centroid of the triangle, whose vertices are (x**_{1 }, y_{1 }, z_{1}) , (x_{2 }, y_{2 }, z_{2}) and (x_{3}, y_{3}, z_{ 3}) are [ (x_{1}+ x_{2}+ x_{3})/3, (y_{1}+ y_{2}+ y_{3}/3) , (z_{1}+ z_{2}+ z_{3}/3) ]

## FAQs on NCERT Solutions Class 11 Maths Chapter 12

### Why are NCERT Solutions Class 11 Maths Chapter 12 Important?

The examples and exercises presented in the NCERT Solutions Class 11 Maths Chapter 12 are based on real-life activities; they teach practical information in addition to the necessary theoretical knowledge. The principles covered in NCERT Solutions are useful for strengthening exam study skills. As a result, these solutions are a valuable resource for learning about the various dimensions and characteristics of three-dimensional geometry.

### Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths Introduction To Three Dimensional Geometry?

NCERT's team ensures that the content gathered in NCERT Solutions Class 11 Maths Introduction To Three Dimensional Geometry is easy to understand and covers all of the major concepts. All of the exercises, examples, and exercise problems have been carefully crafted to assist students in getting a quick and effective understanding of the various topics. As a result, students would benefit from making use of this fantastic resource and by practicing all of the questions in order to assimilate the fundamental principles of three-dimensional space.

### Why Should I Practice NCERT Solutions Class 11 Maths Introduction To Three Dimensional Geometry Chapter 12?

The NCERT solutions are prepared by eminent scholars after a lot of research, and also their intention is to present the matter in an easily understandable language. The CBSE board too highly recommends these solutions for study; hence the probability of the questions landing up in the board examinations is high. Also, the students can learn a strategic approach towards problem-solving by referring to the NCERT Solutions Class 11 Maths Introduction To Three Dimensional Geometry Chapter 12.

### What are the Important Topics Covered in Class 11 Maths NCERT Solutions Chapter 12?

The important topics covered in the NCERT Solutions for Class 11 math Chapter 12 includes a description of the rectangular Cartesian coordinate system, how to identify the coordinates of a location in space, and how to compute the distance between two points. What is the section formula, and how may it be used to verify point collinearity, the formula for finding the coordinates of the mid-point of the line segment, and to find the coordinates of the centroid of the triangle, are also explained in detail.

### How Many Questions are there in NCERT Solutions Class 11 Maths Chapter 12 Introduction To Three Dimensional Geometry?

The NCERT Solutions Class 11 Maths Chapter 12 Introduction To Three Dimensional Geometry Chapter 12 has 14 questions, of which 9 are easy, 3 are moderately easy, and 3 are long answer type questions. There is also a miscellaneous exercise at the end of the chapter whose problems combine all of the concepts learned in the chapter. It has 5 questions, which will be advantageous for the students to learn higher-level math.

### How CBSE Students can utilize NCERT Solutions Class 11 Maths Chapter 12 effectively?

In the NCERT solutions, there are several activities and examples that students should practice because this will help them build the necessary logic to understand the chapter well. After that, they must solve all of the exercise problems. Each activity, example, and problem question will assist students in exploring various aspects of three-dimensional geometry, allowing them to use the NCERT Solutions Class 11 Maths Chapter 12 effectively.

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