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

NCERT Solutions for Class 11 Maths Chapter 12 provide you with a solid conceptual base for all the topics as per CBSE Class 11 Maths syllabus. For your better conceptual understanding, all the formulae and questions have been provided with detailed explanations. The solutions have been provided in a very simplified language with the help of examples so that you have a better understanding of this chapter.

In chapter 12, you shall learn the basic concepts of geometry in the three-dimensional space. This chapter covers the concepts of coordinate axes and coordinate planes in three dimensions, coordinates of a point, distance between the two points and section formula. The chapter is easy to understand and also proves helpful for you to grasp the topic to make your foundations strong. There are only 4 exercises in the chapter with a total of 20 questions.

Our subject matter experts facilitate you with the smooth and precise understanding of concepts through NCERT Solutions. Each question of this chapter has been provided with a detailed step by step explanation so that you have a better understanding. Apart from the solved exercises, you can find exercise discussion of the chapter and a short summary below.

Important Points for NCERT Solutions for Class 11 Maths Chapter 12

Chapter 12 of NCERT Solutions for Class 11 Maths book gives you an introduction to three-dimensional geometry. This chapter is divided into 5 different sub-topics that include coordinate axes and coordinate planes in three-dimensional space, coordinates of a point in space, distance between the two points and section formula.

There are some solved examples given in the textbook which you are advised to practice. A miscellaneous exercise is also present at the end of this chapter that contains additional questions which cover all the topics in it so that it must be practised. It will help you to clear your concepts on the introduction to three-dimensional geometry.

Important Terms in Three-Dimensional Geometry

  • Three mutually perpendicular lines in space define three mutually perpendicular planes, called Coordinate Planes, which in turn divide the space into eight parts known as Octants and the lines are known as Coordinate Axes; 
  • Coordinates of a point lying on x-axis, y-axis & z-axis are of the form (x,0,0), (0, y,0) and (0,0, z) respectively; 
  • Coordinates of a point lying on xy – plane, yz – plane and xz – the plane is of the form (x,y,0), (0,y,z) and (x,0,z) respectively; 
  • Coordinates of a point P are the perpendicular distances of P from the three coordinate planes YZ, ZX and XY respectively; 
  • The reflection of the point (x, y, z) in xy – plane, yz – plane and xz plane is (x, y, -z), (-x, y, z) and (x, -y, z) respectively.

Exercise-wise discussion of NCERT Solutions for Class 11 Maths Chapter 12

  1. This chapter consists of three exercises to be solved by the learners. 
  2. Exercise 12.1 includes 4 questions to be practised. The questions are based on coordinates. This is the simplest exercise in the entire chapter. 
  3. Exercise 12.2 includes 5 questions to be practised. The questions are based on finding the distance between two points and the vertices of a triangle, parallelogram etc. 
  4. Exercise 12.3 includes 5 practical questions to be solved on the section formula and coordinates of a point. 
  5. There is also a miscellaneous exercise at the end of the chapter which consists of 6 questions for practice.

Benefits of NCERT Class 11 Solutions for Chapter 12 by Instasolv

The NCERT solutions for class 11 maths chapter 12 give you detailed explanations for all the questions which help you while you prepare for class 11 CBSE exams. The NCERT solutions are prepared in an organized manner and all the topics and questions are covered in a systematic way. All problems are simplified and explained in an easy way to make learning easy for you. The solutions provided in this chapter help you while preparing your assignments and also while preparing for entrance exams.