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NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry - PDF Download

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Team eSaral

eSaral Academic and Editorial Team

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Summary

NCERT Solutions for Class 11 Maths Chapter 11 cover Three Dimensional Geometry — including coordinate axes in 3D space, coordinates of a point, distance between two points, and the section formula. Exercise 11.1 has 4 questions, Exercise 11.2 has 5 questions, and the Miscellaneous Exercise has 4 questions. A free PDF is available below.

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NCERT solutions for class 11 maths chapter 11 provides an introduction to the fundamental principles of three-dimensional geometry. In this chapter you will learn about the Cartesian coordinate system, distance formula, and section formula, as well as how to find coordinates of a point in a space. You will gain a better understanding of geometric forms and patterns through the combination of the strengths of algebra and coordinate geometry through the use of relevant practical exercises. You will get to understand the practical applications of the three coordinates and how they can be applied to find measures such as point distances and angles between lines that are fundamental to the understanding of shapes such as triangle and parallelogram.

NCERT solutions for class 11 maths chapter 11 are developed by highly qualified maths teachers of eSaral, allowing students to solve any question with ease. These NCERT Solutions provide comprehensive answers to all unsolved questions from exercises. Additionally, the examples for class 11 offer helpful solutions for enhancing conceptual understanding. Students of class 11 maths can download these NCERT free PDF to improve their comprehension of Introduction to Three Dimensional Geometry and practice questions including in chapter.

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Important Topics covered in Chapter 11 - Introduction to Three Dimensional Geometry

NCERT solutions for class 11 math chapter 11 describes 3D space in the Cartesian coordinate system using x, y and z axes. Any point in 3D space can be defined using these coordinates.The following are the topics of chapter 11 Introduction to 3 Dimensional Geometry. 

11.1 Introduction

11.2 Coordinate Axes and Coordinate planes in Three Dimensional Space

11.3 Coordinates of a point in Space

11.4 Distance between two points

11.1 Introduction - In this section, you’ll learn about coordinate axes, real-world coordinate planes, point coordinates related to three coordinate planes and three-dimensional geometry.

11.2 Coordinate Axes and Coordinate planes in Three Dimensional Space - This section explains what a rectangular coordinate system is, how to name a coordinate plane and how to use different notation in coordinate planes.

11.3 Coordinates of a point in Space - In this section, you’ll learn about the coordinate system in space, and the [x], [y] and [z] coordinate systems with a few examples.

11.4 Distance between two points - In this section, the distance formula is used to measure the distance between 3 points in a 3D coordinate system along with a few solved questions.

If you have an object P in the coordinate space, you can use the distance formula to figure out the distance between P and the three axes (x, y, z).

NCERT Solutions for Class 11 Maths Chapter 11 Exercises

NCERT solutions for class 11 maths chapter 11 Introduction To Three Dimensional Geometry Exercise-wise Detailed Analysis is provided below.

Exercise 11.1

4 Questions & Solutions

Exercise 11.2

5 Questions & Solutions

Miscellaneous Exercise 

4 Questions & Solutions

Benefits of Downloading The NCERT Solutions for Class 11 Maths Chapter 11 - Introduction to Three Dimensional Geometry

NCERT solutions for class 11 maths chapter 11 - Introduction to 3 Dimensional Geometry provide a structured and comprehensive way to understand 3D space and its mathematical representations. Here, we will discuss the major benefits of downloading and using these solutions to improve your learning.

  1. Students can download and analyze these NCERT solutions to gain insight into concepts like coordinates, line distance, and more.
  2. In NCERT solutions, there are a bunch of different formulas, concepts, and the answers in this chapter give you a step-by-step plan on how to solve questions effectively.
  3. Practicing these NCERT solutions by eSaral helps students learn how to solve problems in a strategic way, which saves them a lot of time on their exams.
  4. Students can review their solutions against the answers provided in the NCERT Solutions by downloading them. This allows them to identify areas of improvement and work on correcting errors.

Frequently Asked Questions

What topics are covered in NCERT Solutions for Class 11 Maths Chapter 11?

Chapter 11 covers four main topics: an introduction to 3D space, coordinate axes and coordinate planes, coordinates of a point in space, and the distance formula between two points. The section formula (internal and external division) is also covered in Exercise 11.2 and the Miscellaneous Exercise.

What is Three-Dimensional Geometry in Class 11 Maths?

Three Dimensional Geometry is the study of points, lines, and shapes in a three-axis coordinate system (x, y, z). Unlike 2D geometry, every point in 3D space requires three values to be located precisely. Class 11 introduces the foundational tools — distance formula and section formula — that are then extended in Class 12 to lines and planes in space.

How many exercises are there in Chapter 11 of Class 11 Maths?

Chapter 11 has three exercises in total: Exercise 11.1 (4 questions), Exercise 11.2 (5 questions), and a Miscellaneous Exercise (4 questions). All 13 questions have detailed step-by-step solutions available in eSaral's free PDF download.

How is the distance formula in 3D different from the 2D distance formula?

The 3D distance formula adds a third term for the z-coordinate. For points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂), the distance is √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]. The 2D formula is the same but without the (z₂−z₁)² term. The logic and structure are identical — only the added dimension changes the calculation.

Is Chapter 11 Three Dimensional Geometry important for JEE Main?

Yes. The distance formula and section formula covered in Class 11 Chapter 11 are direct prerequisites for JEE Main's 3D geometry questions. JEE Main typically includes questions on lines and planes in 3D (Class 12 content), but those questions assume full command of the Class 11 coordinate and distance concepts. Building accuracy here prevents errors in the more advanced problems.

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eSaral Academic and Editorial Team

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