Read and download NCERT Class 12 Maths Three Dimensional Geometry in NCERT book for Class 12 Mathematics. You can download latest NCERT eBooks chapter wise in PDF format free from Studiestoday.com. This Mathematics textbook for Class 12 is designed by NCERT and is very useful for students. Please also refer to the NCERT solutions for Class 12 Mathematics to understand the answers of the exercise questions given at the end of this chapter
NCERT Book for Class 12 Mathematics Chapter 11 Three Dimensional Geometry
Class 12 Mathematics students should refer to the following NCERT Book Chapter 11 Three Dimensional Geometry in Class 12. This NCERT Book for Class 12 Mathematics will be very useful for exams and help you to score good marks
Chapter 11 Three Dimensional Geometry NCERT Book Class 12
11.1 Introduction
In Class XI, while studying Analytical Geometry in two dimensions, and the introduction to three dimensional geometry, we confined to the Cartesian methods only. In the previous chapter of this book, we have studied some basic concepts of vectors. We will now use vector algebra to three dimensional geometry. The purpose of this approach to 3-dimensional geometry is that it makes the study simple and elegant*.
In this chapter, we shall study the direction cosines
and direction ratios of a line joining two points and also discuss about the equations of lines and planes in space under different conditions, angle between two lines, two planes, a line and a plane, shortest distance between two skew lines and distance of a point from a plane. Most of the above results are obtained in vector form. Nevertheless, we shall also translate these results in the Cartesian form which, at times, presents a more clear geometric and analytic picture of the situation.
11.2 Direction Cosines and Direction Ratios of a Line
From Chapter 10, recall that if a directed line L passing through the origin makes angles α,β andγ with x, y and z-axes, respectively, called direction angles, then cosine of these angles, namely, cosα, cos β and cos γ are called direction cosines of the directed line L.
If we reverse the direction of L, then the direction angles are replaced by their supplements,i.e.,∏ −α , ∏ − β and∏ − γ. Thus, the signs of the direction cosines are reversed.
Please refer to attached file for NCERT Class 12 Maths Three Dimensional Geometry
| NCERT Class 12 Maths Relations and Functions |
| NCERT Class 12 Maths Inverse Trigonometric Functions |
| NCERT Class 12 Maths Matrices |
| NCERT Class 12 Maths Determinants |
| CBSE Class 12 Maths Continuity and Differentiation |
| NCERT Class 12 Maths Continuity and Differentiability |
| NCERT Class 12 Maths Application of Derivatives |
| CBSE Class 12 Maths Integrals |
| NCERT Class 12 Maths Integrals |
| NCERT Class 12 Maths Application of Integrals |
| NCERT Class 12 Maths Differential Equations |
| CBSE Class 12 Maths Vector Algebra |
| NCERT Class 12 Maths Vector Algebra |
| NCERT Class 12 Maths Three Dimensional Geometry |
| NCERT Class 12 Maths Linear Programming |
| NCERT Class 12 Maths Probability |
| NCERT Class 12 Mathematics Answers and Solutions |
| NCERT Class 12 Mathematics Answers and Solutions |
| NCERT Class 12 Mathematics Proofs In Mathematics |
| NCERT Class 12 Mathematics Mathematical Modeling |
Mathematics NCERT Book Class 12 Chapter 11 Three Dimensional Geometry
The above NCERT Books for Class 12 Mathematics Chapter 11 Three Dimensional Geometry have been published by NCERT for latest academic session. The textbook by NCERT for Chapter 11 Three Dimensional Geometry Mathematics Class 12 is being used by various schools and almost all education boards in India. Teachers have always recommended students to refer to Chapter 11 Three Dimensional Geometry NCERT etextbooks as the exams for Class 12 Mathematics are always asked as per the syllabus defined in these ebooks. These Class 12 Chapter 11 Three Dimensional Geometry book for Mathematics also includes collection of question. We have also provided NCERT solutions for Class 12 Mathematics which have been developed by teachers of StudiesToday.com after thorough review of the latest book and based on pattern of questions in upcoming exams for Class 12 students.
NCERT Book Class 12 Mathematics Chapter 11 Three Dimensional Geometry
The latest NCERT book for Chapter 11 Three Dimensional Geometry pdf have been published by NCERT based on the latest research done for each topic which has to be taught to students in all classes. The books for Class 12 Mathematics Chapter 11 Three Dimensional Geometry are designed to enhance the overall understanding of students. All Class 12 NCERT textbooks have been written in an easy to understand language which will help to enhance the overall level of Class 12 students.
Chapter 11 Three Dimensional Geometry NCERT Book Class 12 Mathematics
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Class 12 Mathematics Chapter 11 Three Dimensional Geometry NCERT Book
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Class 12 Chapter 11 Three Dimensional Geometry NCERT Book Mathematics
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