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

Class 11 Maths NCERT Solutions Chapter 12 Ex 12.1 consistes of all the answers for the chapters of NCERT Class 11 paper - Three Dimensional Geometry. The Exercise 12.1 Class 11 solutions are prepared by some of the best educators in the country. These solutions are simple and ideal for studying. These solutions provide you with a detailed explanation of the entire chapter. You can start your preparation by downloading the Exercise 12.1 Class 11 Maths Solution PDF.

**Study without Internet (Offline)**

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

## Access NCERT Solutions for Class 11 Maths Chapter 12 - Introduction to Three Dimensional Geometry

Exercise 12.1

Refer to pages 1-3 for exercise 12.1 in the PDF

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

Ans: We know that, the coordinates of any point on the $x$-axis will be as $\left( {x,0,0} \right)$.

Thus, if a point is on the $x$-axis, then its $y$-coordinate will be $0$ and $z$-coordinate will be 0.

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

Ans: We know that, the coordinates of any point in the XZ-plane will be as $\left( {x,0,z} \right)$.

So, in the XZ- plane $y = 0$.

Thus, if a point is in the XZ- plane then the coordinate of $y$will always be 0.

Hence, its $y$-coordinate is 0.

3. Name the octants in which the following points lie:

$\left( {{\mathbf{1,2,3}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( {1,2,3} \right)$ lies in the first octant.

$\left( {{\mathbf{4, - 2,3}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( {4, - 2,3} \right)$ lies in octant IV.

$\left( {{\mathbf{4, - 2, - 5}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( {4, - 2, - 5} \right)$ lies in octant VIII.

$\left( {{\mathbf{4,2, - 5}}} \right)$

Ans: We have the following table,

From the above table, the point $\left( {4,2, - 5} \right)$ lies in octant V.

$\left( {{\mathbf{ - 4,2, - 5}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 4,2, - 5} \right)$ lies in octant VI.

$\left( {{\mathbf{ - 4,2,5}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 4,2,5} \right)$ lies in octant II.

$\left( {{\mathbf{ - 3, - 1,6}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 3, - 1,6} \right)$ lies in octant III.

$\left( {{\mathbf{ - 2, - 4, - 7}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 2, - 4, - 7} \right)$ lies in octant VII.

4. Fill in the blanks:

(i) The x-axis and y-axis taken together determine a plane known as ___________ .

Ans: In XY-plane, $z = 0$.

Hence, 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 _____________ .

Ans: In XY-plane, $z = 0$.

Let $x$-coordinate be $x$ and $y$-coordinate be $y$.

Hence, the coordinates of points in the XY-plane are of the form $\left( {x,y,0} \right)$.

(iii) Coordinate planes divide the space into ______ octants.

Ans: Coordinate planes divide the space into 8 octants.

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

The Class 11th Maths Chapter 12 Exercise 12.1 NCERT Solution is prepared by top teachers with years of teaching experience. These experienced teachers know exactly what is needed and they have prepared the notes exactly. They are subject-matter experts and they know which are the most important focus points. Furthermore, they are very well acquainted with the teacher's psychology. As a result, a vast majority of the question paper are already covered in this Exercise 12.1 Class 11 notes. This note is prepared as per the CBSE guidelines and everything in the syllabus is covered in this note.

There are no rewards for guessing the fact that Class 11 Maths syllabus is gigantic and there are a plethora of things to cover. From Determinants to Derivatives, from Conics to Boolean Algebra, the syllabus is vast and is equally concept-oriented. There are so many things to cover but you only have a limited time. This is where NCERT Solutions come into the picture. Notes such as Exercise 12.1 Class 11 Maths NCERT Solutions will provide you the perfect base for going forward.

Talking of the importance of CBSE Class 11 Maths syllabus, the first thing that comes to mind is Three Dimensional Geometry. This is perhaps one of the most essential chapters in the syllabus. This Chapter will put your application and conceptual understanding at test. This is why one of the main priorities was to make all the concepts clear. The NCERT Class 11 Maths Chapter 12 Exercise 12.1 specially focus on making the concepts clear with step-by-step solutions.

After preparing from this note, you will feel more confident as your concepts will be clear. With a clear concept, you can solve all kinds of problems. Once you understand the framework, application is not that difficult. This is where practice is of utmost importance when it comes to a subject like CBSE Class 11 Maths. Unlike other subjects, Maths is something that you should practice once every day. However, it is true that there are a plethora of chapters and you cannot practice all. The time is very limited. This is where NCERT Solutions like Class 11 Maths Ch 12 Ex 12.1 will help your cause. You will get proper revision notes for all the chapters prepared by some of the most experienced and renowned faces in the education industry. You need to visit Vedantu's website or simply download the official Vedantu app to learn more from the most influential teachers.

Some Useful Education Tips to Score Good Marks in Maths

Class 11 means that you are standing at the most pivotal part of your career. You are just a step away from the Class 12 exam. The scores you obtain now will stay with you forever. This is why it is of utmost importance to lay maximum focus. For a subject like Maths, you need to concentrate, understand, and practice. There is no denying the fact that Maths is one of the most feared subjects. The term Maths phobia or Mathematical anxiety is very common among Class 11 students. At the same time, Maths is one of the most scoring subjects.

The best way to combat anxiety and fear related to this subject is by loving it. Maths is an extremely interesting subject and you will definitely fall in love with it if you start understanding the concepts, ideas, and applications. The idea is very clear - understand the concepts and improve your preparation.

Here are some key tips that will certainly help you to master this subject:

Plan Your Day - The NCERT Class 11 syllabus is humongous. However, you cannot afford to score excellent in a particular subject only. The board result will showcase the aggregate marks of all the subjects. As a result, you cannot spend an entire day studying English or practicing Maths. This is why you need to break your day into several parts and make the most of the available time.

Understanding First - Maths is a subject which is entirely concept-based. You can certainly score excellent marks if your concepts are clear. This is why understanding not learning should always be the first priority. The Class 11 Ch 12 Ex 12.1 Maths NCERT Solutions is solely focused on bolstering your concepts with a focus on clear understanding.

Practice Matters - Regular practice is very important. You can practice the same sums but every time you will be learning something new. This is what practice does when it comes to a concept-oriented subject such as Maths. Practice regularly to strengthen your base. Chapters like Three Dimensional Geometry is entirely practice-oriented and it is exactly what you need for improving the base. When it comes to practice, you need the best notes. This is where NCERT Solutions Class 11 Maths Chapter 12 Ex 12.1 comes into the frame. Consult the notes created by the experts and start practicing.

Solve Mocks - Practice papers are very important. Keep solving mock papers and previous years papers to get a clear grip. It will certainly help you to keep calm and boost your confidence. This will certainly take your exam preparation to the next level in a matter of time.

Start your exam preparations by downloading the NCERT Solutions Class 11 Maths Chapter 12 Ex 12.1 revision paper solved by Vedantu's top Maths experts. Download the free PDF to embrace smart and efficient learning.

Vedantu's main priority is to help young students to achieve their dreams. This is why you will find free PDFs on the official Vedantu site curated by top educational experts with more than a decade of experience in teaching a particular subject. All of these are free so that it is easily accessible by all the students in the country. Success is for all. The difference is in the effort invested. Vedantu aims to plan the first seeds of your success with free educational content.

### Why Vedantu?

Vedantu is India's biggest and most successful online educational platform. Vedantu is the success behind hundreds and thousands of students achieving their dreams every year. A big reason behind the tremendous success of Vedantu is their student-centred approach. At Vedantu, students come first.

From Maths to Geography, from Physics to English, from Social Science to Biology, this online education platform is filled with subject-matter experts. Vedantu's large pool of the best teachers certainly make a difference. A vast majority of the teachers have years of teaching experience and they also come from the best educational institutions in India. They have tremendous subject knowledge and they know exactly which part of the syllabus carries what importance. This is why in notes such as Class 11 Maths NCERT Solutions Chapter 12 Ex 12.1 - Three Dimensional Geometry you will see that a lot of focus and explanation is invested in certain sections. Those sections are more likely to appear in your exam paper. As a result, your preparation is perfectly balanced and you are unknowingly putting more effort into the most important areas of the chapter which is incredible news for scoring fantastic marks.

Embrace smart learning with Vedantu. Download the official app or visit the website to get started. Best of Luck!