NCERT Solutions Class 12 Mathematics Chapter 11 Three-Dimensional Geometry
Class 12 Mathematics syllabus has a total of 13 essential chapters. Chapter 11 is on Three-Dimensional Geometry, which is a continuation of the chapter: Vector Algebra. The important topics covered are the distance between two points, section formulae and coordinates of a point in space. Geometry guides you in deciding how to design houses and buildings in different geometric shapes in the real world. NCERT Solutions Class 12 Mathematics Chapter 11 helps students find answers to the questions necessary for final exams. This chapter makes the process of learning Three-Dimensional Geometry simpler. This would be helpful for you in your daily practice sessions and while completing homework assignments. The step-by-step walkthrough of the solution is self-explanatory.
NCERT Solutions Class 12 Mathematics Chapter 11 assists students:
- In studies.
- Increases competency levels.
The solutions provided come in handy for completing the Classwork and preparing for the exams. This focuses on:
- 3D shapes involving three coordinates, namely X, Y, & Z coordinates.
- The shapes that absorb space are called 3D shapes.
- They are rigid shapes having three dimensions: length, width, and height.
Three-Dimensional Geometry plays an essential role in exams as multiple questions are included from this chapter in the assessment. NCERT Solutions Class 12 helps students solve complex Three-Dimensional Theories in more straightforward ways. This gives students a solid introduction to Three-Dimensional Mathematics while studying geometry in three different directions.
Key Topics Covered In NCERT Class 12 Mathematics Chapter 11
This is a practical lesson that provides better suggestions for implementing formulas. In this account, we will explore different formulas, examples, and theories thoroughly to help students build a solid Mathematical foundation. NCERT Solutions Class 12 Mathematics Chapter 11 applies many real-life examples to deliver students a better understanding of the subject.
Studying Geometry provides many basic skills and builds:
- logical thinking.
- Analytical reasoning.
- Problem-Solving Skills.
The main topics covered NCERT Solutions for Class 12 Mathematics Chapter 11 – Three-Dimensional Geometry are
| Serial No |
Topic |
| 1 |
Introduction |
| 2 |
Coordinate Axes and Coordinate Planes in Three-Dimensional Space |
| 3 |
Coordinates of a Point in Space |
| 4 |
Distance Between Two Points |
| 5 |
Section Formula |
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Introduction
The theory covers the notes prepared as per the CBSE syllabus (2022–2023) and the NCERT curriculum. Prime topics covered in NCERT Solutions Class 12 Mathematics Chapter 11 are Direction Cosine and Direction Ratios of a line joining two points. You can also consider the equation of lines and planes in space under different conditions, the angle between line and plane, space between two lines etc. NCERT Solutions Class 12 Mathematics Chapter 11 will help you practice the formulas thoroughly to know the subject well. This topic has been introduced in Mathematics to find different shapes and figures. In the real world, all the objects are in a three-dimensional form. For example, household objects like tables, kitchen utensils, beds etc., have 3D geometry. You would learn the latest advanced version of 3D geometry in the 12th standard.
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Coordinate Axes and Coordinate Planes in Three-Dimensional Space
The three coordinate axes of a rectangular Cartesian coordinate system are the x-axis, y-axis, and z-axis. These lines are three mutually perpendicular lines. NCERT Solutions Class 12 Mathematics Chapter 11 further explains that the Three-Dimensional Geometry shape has a face, an edge, and a vertex. The size of these forms has been decided by the area they occupy. Space exists in 2D structures, whereas surface space exists in three-dimensional shapes. The opening of all the faces of a three-dimensional form is the surface area, cube, cuboid, cone, and Cylinder shapes that can be seen around us. A coordinate plane is formed by the pair of axes of the three-dimensional coordinate system x, y, and z. NCERT Solutions Class 12 Mathematics Chapter 11 explains this coordination in detail.
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Coordinates of a Point in Space
NCERT Solutions Class 12 Mathematics Chapter 11 explains a three-dimensional space called 3-space or tri-dimensional space. The point in the space of a geometric setting that contains three values, x, y and z, is required to determine the position of an element. This performs as a three-parameter physical world model where tangible matter exists. These three values are selected from the term’s width, height, depth, and length. Just as two-dimensional space consists of many boundless lines, three–dimensional space contains infinitely many planes. These planes are of a particular value. For example, the XY plane consists of the x-axis and y-axis, the YZ plane, which consists of y-axis and z-axis and the XZ plane, which holds the x-axis n z-axis. NCERT Solutions Class 12 Mathematics Chapter 11 provides many examples for a more straightforward understanding of the above-mentioned points.
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Distance Between Two Points
Distance between two points is the length of the line segment that connects the two given points. NCERT Solutions Class 12 Mathematics Chapter 11 preferably uses a formula in Mathematics to calculate the distance between the two points in the coordinate plane. By replacing those points in the formula, we can get the distance between two points. To find out the position of a point in a plane, we require a pair of the coordinate axis. The distance of the point through the x-axis from the Centre is called the x-coordinate. The distance of the point across the y-axis from the starting point is called y-coordinate. The ordered point x and y represents the coordinate of the point.
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Section Formula
The section formula has been applied to find out the coordinates of a point. The coordinates of a point in the three–dimensional space are used to locate the point given in the system. This can decide the point that divides a line internally into a specific ratio. Section formula could be divided into internal division formula and external division formula. NCERT Solutions Class 12 Mathematics Chapter 11 also focuses on exceptional cases of section formulas like the midpoint formula and trisection points. Section formulas in three-dimensional can be used to gain more valuable results in
- Coordinates of the centroid of a triangle.
- Collinearity of three points.
NCERT Solutions Class 12 Mathematics Chapter 11 provides detailed clarity of internal and external section points.
NCERT Solutions Class 12 Mathematics Chapter 11 – Exercises and Answer Solutions.
The exercise and solutions paper are available on the Extramarks website. These questions will clear all doubts, help students understand the concept better, and quickly solve the Mathematical problems. NCERT Solutions Class 12 Mathematics Chapter 11 includes questions according to the latest CBSE syllabus of 2022-23.
Exercise 11.1 – 5 Questions (Short Questions)
Exercise 11.2 Coordinate Axes and Coordinate Planes in Three-Dimensional Space – Questions & Solutions refer to the below link.
Exercise 11.2 – 17 Questions (9 Short Questions and 8 Long Questions)
Exercise 11.3 Coordinates of a Point in Space – Questions & Solutions click on the below link.
Exercise 11.3 – 14 Questions (5 Short Questions and 9 Long Questions)
Exercise 11.4 Distance Between Two Points – Questions & Solutions click here to know more.
Exercise 11.5 Section Formula – Questions & Solutions refer to the link below.
Along with Class 12 Mathematics solutions, you can explore NCERT Solutions on our Extramarks website for all primary and secondary Classes. NCERT Solutions Class 1, NCERT Solutions Class 2, NCERT Solutions Class 3, NCERT Solutions Class 4, NCERT Solutions Class 5, NCERT Solutions Class 6, NCERT Solutions Class 7, NCERT Solutions Class 8, NCERT Solutions Class 9, NCERT Solutions Class 10, NCERT Solutions Class 11, NCERT Solutions Class 12.
NCERT Exemplar for Class 12 Mathematics
NCERT Exemplars are practice books that include additional higher-level questions and are meant to aid meticulous learning. They are mainly used for competitive exams. These topics are up to date, consisting of different topics explained in every chapter of the Class 12 Mathematics book. Students can click on the links provided by Extramarks for these Exemplar questions and answers for Class 12 Mathematics chapter wise notes.
Considering the standard and variety, practising Exemplar problems is essential for school boards and competitive examinations. Students can perfectly evaluate themselves by working on these problems and altering their problem-solving skills for future examinations. NCERT Solutions Class 12 Mathematics provides a series of exemplar solutions for Class 12 for detailed clarification to all questions given in the NCERT exemplar Class 12 books.
Key Features of NCERT Solutions for Class 12 Mathematics Chapter 11
To score well in competitive exams, one should have a strong command in Mathematics. The NCERT books present you with demanding questions that improveyour analytical skills and give you sufficient exposure to all kinds of questions in any of these exams. Our application is highly beneficial for your preparation for the following reasons.
- NCERT Solutions Class 12 Mathematics answers to all numerical problems in the textbook are given with a step-by-step simplification.
- Free unlimited access.
- Highly detailed solutions to all the theoretical as well as logical reasoning questions from the NCERT Mathematics textbook of Class 12 that are verified by respective experts of the subject.
- The reputed teachers’ accurate and straightforward answers cover all the complex and specific topics.
- The material provided by NCERT helps students to score remarkably in the exams.