NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry (Ex 12.1) Exercise 12.1

An official government institution called the National Council of Educational Research and Training (NCERT) was established to help India’s schools improve their educational standards. NCERT is in charge of producing and spreading textbooks to create a system of universal education. To assist students with their studies, it also creates educational kits and multimedia digital assets. NCERT textbook questions are used in almost all the Central Board of Secondary Education and state board schools. There are several exercises in the NCERT textbook. These exercise questions should be answered attentively by students. The questions in the final examination are based on these NCERT exercise problems. Students should therefore, at the very least, practise all of the exercise problems from the textbooks before the examination. Students frequently encounter issues and are unable to determine the solutions. To help them, Extramarks has supplied thorough, step-by-step NCERT solutions for all the classes. Additionally, by using these solutions, students will be able to better plan their responses from the perspective of the examination, which will help them get better examination grades.

The CBSE’s primary role is to curate question papers for students.CBSE gives primary preferenceto the NCERT textbooks. The question papers are created by the CBSE according to the NCERT Board exam guidelines. Therefore, students must study from the NCERT textbooks to practise every question that can appear on the question paper to score high marks in their examination. There are a vast number of concepts and formulas in Mathematics, and students often consider it a complex subject. Students often experience difficulties while trying to complete the questions.As a result, NCERT Solutions for each class are available to help them.. To write their answers more effectively from the viewpoint of the examination and receive higher grades, students will also benefit from these solutions.

While developing the question paper, NCERT textbooks are primarily focused on CBSE.Students are advised to use NCERT Solutions.These textbooks do not contain detailed solutions, therefore, students often face difficulty understanding the solutions properly. As a result, the Extramarks website provides students with detailed NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1.Top teachers with years of teaching experience created the NCERT Solutions for Class 11 Maths, Chapter 12, Exercise 12.1.These knowledgeable instructors have precisely prepared the notes and know exactly what is required. They have in-depth knowledge of the subject and are aware of the crucial focal points.As a result, NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1 cover the vast majority of exam questions. Everything on the syllabus is covered in this note, which was written following CBSE requirements.

Students will feel more assured after studying from NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1  because their concepts will be clear. Students can solve any problem if they have a clear concept. Application is not that tough if students comprehend the structure.Practise is essential when it comes to a topic like NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1. Mathematics is a topic that students should practice once per day, unlike other subjects. There are, however, a lot of chapters, and students cannot practise them all. Students have very less time available, so they can improve their practice by using NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1.

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry (Ex 12.1) Exercise 12.1

Class 11 Maths syllabus is vast and there are numerous topics to cover. The curriculum is extensive and similarly concept-oriented, covering everything from Determinants to Derivatives, from Conics to Boolean Algebra. There are a lot of topics to discuss, but students only have a limited amount of time. NCERT Solutions play a role in this situation. The NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 will give students the ideal foundation for moving forward. The importance of CBSE Class 11 Maths Chapter 12 Exercise 12.1 is immediately apparent when discussing it and it is one of the most important chapters of the course. Students’ application and conceptual comprehension will be tested in this chapter. With step-by-step solutions offered by the Extramarks website, the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 focus especially on making the concepts apparent.

Concerning a topic like an Exercise 12.1 Class 11 Maths, practise is crucial in this area. Mathematics is a topic that students should practise once per day, unlike other subjects. There are, however, a lot of chapters, and students cannot practise them all. There is not much time Students can understand the concept by using NCERT Solutions, such as NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1.  For each chapter, students will receive thorough revision notes that have been written by some of the most seasoned and well-known educators in the education sector. To learn more from the most well-known teachers, students can get registered on the Extramarks website or just download the Extramarks app.

The Three-Dimensional Geometry mentions the three coordinate axes of a rectangular Cartesian coordinate system, which are axis X, axis Y, and axis Z. Three of these lines are perpendicular to one another. The position of the point in the Coordinate plane is determined by the values of the coordinate axes.  There are many different concepts presented in the chapter. All of the chapters have comprehensive revision notes created by some of the most experienced and well-known experts at Extramarks. To learn more about Ex 12.1 Class 11, students must refer to the Extramarks website. The student’s position in Class 11 indicates that their career is at its most critical point. The marks students score in Class 11 are always of great importance. It is therefore imperative that students pay close attention to this matter. Students must focus, comprehend, and practise to succeed in a topic like Mathematics. It is undeniable that Mathematics is one of the subjects that students are most afraid of.

Mathematics is also one of the subjects that require mental skills. The easiest method to overcome the fear associated with this topic is to understand it. If students start to comprehend the concepts, ideas, and applications, they will undoubtedly understand Mathematics. Understanding the topics and strengthening the preparation is the clear-cut message.

Mathematics requires skills and abilities.If the students’ concepts are clear, they can achieve good grades.This is why the top emphasis should always be on comprehending rather than learning. A primary objective of Class 11 is to strengthen the concepts while emphasising a thorough understanding of them.

The NCERT Mathematics textbooks cover a wide range of concepts, so to succeed in their examinations, they should refer to the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1. The NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 are not included in NCERT textbooks. Due to unclear concepts, students frequently have trouble understanding concepts correctly. Students can therefore access reliable NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 from the Extramarks website. Students who struggle to understand a concept properly might use the NCERT Solutions provided by Extramarks. Due to the fact that the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 on the Extramarks website are produced by subject matter experts and the solutions provided are authentic in nature. Students can understand the concepts completely and achieve good marks in their exams, the solutions are validated and explained in a step-by-step manner.

Mathematics is a conceptual subject. The NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 can help to strengthen students’ concepts while emphasising crystal-clear comprehension. Consistent practise is crucial.  A subject like Mathematics requires a lot of practise by students to clearly understand each concept. They will always learn something new, even if they repeatedly practise the same questions. When it comes to a concept-based subject like Mathematics, practise makes perfect. Regular practise will build students’ foundations.

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

Mathematics is one of the most crucial subjects for a student to study throughout their academic career.  It is one of the important subjects for students who choose the Science and Commerce stream and are registered under the Central Board of Secondary Education.  Mathematics is regarded as one of the most difficult subjects by students.Students are not just supposed to thoroughly comprehend the mathematical concepts;  they also need to practise the questions as much as they can. Despite learning and mastering each subject in the curriculum, a lack of exercise completion is seen among students. Consequently, they are at a disadvantage when they appear for their annual examination. To achieve higher scores in examinations, they must solve this problem. The Extramarks website offers NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 to assist in solving this issue.

Students can apply the concepts from the chapter in a clearer and more precise way by using the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1. The thorough and error-free  NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 are created by highly qualified teachers from the Extramarks website. The cognitive abilities of Class 11 students are taken into consideration as they build these answers. In order to make  NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 simpler, the solutions have been broken into smaller, more manageable steps. Teachers usually emphasise the need for thorough, step-by-step solutions.

Students should carefully follow the directions in the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 for the best examination results. Many of the formulas in the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 are challenging. The majority of students find it challenging to comprehend and retain material from NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1, which prevents them from using them to answer the exercises’ questions. However, it will be simpler for the students to recall the formulas and use them correctly if they practice the step-by-step solutions in the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1. By completing the NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1, students gain the necessary experience to successfully complete the mathematics question paper in the annual examinations.Using the NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1, students can become acquainted with the types of questions that will be asked in the yearly examination.

CBSE Solutions for Class 11 Maths Chapter 12 – Introduction to Three Dimensional Geometry Exercise 12.1

All of the solutions to the chapters of the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 are available to students on the Extramarks website. Some of the greatest experts have curated the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1. These answers are straightforward and are of great help to students. These solutions give students a thorough breakdown of the whole chapter. The teachers at Extramarks are well-versed in their subject areas, and moreover, Extramarks offers live classes to students who are registered on the website or mobile application.

Students can clearly understand the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 from the teachers and can even clear their doubts. The chapter named – Three Dimensional Geometry is termed one of the most important chapters, therefore it is required for students to fully comprehend the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1. Extramarks provides detailed NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 and offers step-by-step solutions to the students. Class 11 is termed the base class for the Class 12 board class; therefore, students should carefully comprehend the concepts to understand the concepts of Class 12 easily.

Why Extramarks?

The Extramarks website is an online platform that provides NCERT Solutions to students. It is an online learning platform that focuses on the pre-school, K-12, higher education, and test prep segments to enable learning anywhere, at any time, by combining education and technology in a creative way.Students can learn  from teachers who are experts in their fields. Extramarks’ learning modules with rich media go into great detail about each topic. It constantly prioritises understanding concepts in detail and quickly, which helps students gradually raise their test scores and achieve their learning objectives. The Learning App offers chapter-based worksheets, interactive activities, unlimited practise questions, and more to help you master all subjects and concepts fully. Students can check their knowledge with adaptive quizzes that have progressively harder difficulty levels, MCQs, and mock examinations to form an upward learning graph. In order to help students get the most out of their learning experience, the Extramarks website keeps tabs on their performance and produces thorough reports and analyses. This performance analysis identifies students’ strong and weak points so that they can strategically organise their studies.

Extramarks provides NCERT Solutions, past years’ papers, sample papers, and other study materials. These resources are available to students who want to excel in their examinations.

Q.1 A point is on the x -axis. What are its y-coordinate and z-coordinates?

Ans. The coordinate of the point on x-axis is (x, 0, 0). The y-coordinate of this point is 0 and that of z-coordinate is also 0.

Q.2 A point is in the XZ-plane. What can you say about its y-coordinate?

Ans. The y-coordinate of a point in XZ-plane is 0.

Q.3 Name the octants in which the following points lie: (1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (– 4, 2, 5), (–3, –1, 6) (2, – 4, –7).

Ans.

 Coordinate Name of octants (1, 2, 3) I (4, –2, 3) IV (4, –2, –5) VIII (4, 2, –5) V (–4, 2, –5) VI (–4, 2, 5) II (–3, –1, 6) III (2, –4, –7) VIII

Q.4 Fill in the blanks:

(i) The x-axis and y-axis taken together determine a plane known as_______.
(ii) The coordinates of points in the XY-plane are of the form _______.
(iii) Coordinate planes divide the space into ______ octants.

Ans.
(i) The x-axis and y-axis taken together determine a plane known as XY-plane.
(ii) The coordinates of points in the XY-plane are of the form (x, y, 0).
(iii) Coordinate planes divide the space into eight octants.

Please register to view this section

1. Which courses do Extramarks offer NCERT Solutions for?

Extramarks offers NCERT Solutions for all the classes, for example, 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.

2. Will the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 help the students in any competitive examinations?

Students can have a solid understanding of the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 for exams such as JEE, NEET etc. Thus, the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 would be useful to the students in competitive examinations.

3. Is the NCERT textbook sufficient to prepare for NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1?

Yes, the NCERT textbook is sufficient to help students develop their fundamental concepts so they can tackle any problems relating to them. But it does not offer any solutions and therefore, for better preparation, students can also practice past years’ papers and sample papers from Extramarks. Students who practice NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 will have a deeper comprehension of the ideas, which will ultimately result in higher grades.

4. Does practising the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 help students do better on the Class 11 examinations?

Yes, students should thoroughly practice each question they come across in the NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1. Each time a student faces a difficult question and tries to solve it, he/she gains a deeper understanding of the material and does better on the examination. As a result, they should review the  NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 since numerous questions from the topic could appear in the examination. Thus, the  NCERT Solutions For Class 11 Maths Chapter 12 Exercise 12.1 should be referred by students.