Miscellaneous Exercise Chapter 12 Class 11: This article includes NCERT Solutions for Chapter 12 of Maths for Class 11 students. The NCERT Solutions for Maths Class 11 are excellent resources that students can use to achieve maximum exam scores. These NCERT Solutions have been created in accordance with the most recent CBSE guidelines.
Embibe provides NCERT Solutions for various exercises of Class 11 Chapter 12 that are thorough, reliable, easy to understand and up-to-date. To ace their CBSE Class 10 exams, students should focus on mastering the in-text questions provided in the NCERT Solutions. We have included the NCERT Solutions for Miscellaneous Chapter 11 Class 12 Maths in PDF format in this article so that students may download them and study them offline. Continue reading to find out more!

Miscellaneous Exercise Chapter 12 Class 11: Overview

It is always important for the students to have an overview of the exercises they are going to learn. Often they do not spend much time solving the miscellaneous exercises. But, to have in-depth knowledge and a deeper understanding of the concepts the miscellaneous exercises are very important.

Class	Class 12
Chapter Name	Introduction to Three Dimensional Geometry
Exercise Title	Miscellaneous Exercise
Topic Name	Coordinate Axes and Coordinate Planes in Three Dimensional Space Coordinates of a Point in Space Distance between Two Points Section Formula
Language	English
Solution Type	In-text Solved Questions
Official Website	https://ncert.nic.in/

NCERT Solutions for Introduction to Three Dimensional Geometry: Download PDFs

Embibe provides the accurate and necessary study materials for Class 11 students to practice and prepare for their examination. Here we have provided the link to download the pdf of chapter 12 class 11 miscellaneous exercise and other exercises:

Practice Class 11 Chapter 12 Maths Exercises

Question: Find the square of the distance between the following pair of points: (2, 3, 5) and (4, 3, 1)
20
Solution: We know that, distance between two points (x1, y1, z1) and (x2, y2, z2) is =(x2-x1)2+(y2-y1)2+(z2-z1)2.

Distance between points (2, 3, 5) and (4, 3, 1):
=(4-2)2+(3-3)2+(1-5)2
=(2)2+(0)2+(-4)2 =4+16 =20 =25
Therefore, the square of the distance between the given two points is 20.
Question: Find the value of K2, if the distance between the pair of points (-3,7,2) and (2,4,-1) is K.
43
Solution: We know that the distance between two points whose coordinates are (x1,y1,z1) and (x2,y2,z2) is (x2-x1)2+(y2-y1)2+(z2-z1)2
Now, Distance between points (-3,7,2) and (2,4,-1) is K=(2+3)2+(4-7)2+(-1-2)2 ⇒K=(5)2+(-3)2+(-3)2 ⇒K=25+9+9 ⇒K=43
Therefore, K2=43.

Question: If the distance between the points (2, -1, 3) and (-2, 1, 3) is k5 then find the value of k.
2
Solution: We know that, distance between two points whose coordinates are (x1,y1,z1) and (x2,y2,z2) =(x2-x1)2+(y2-y1)2+(z2-z1)2

Distance between points (2,-1,3) and (-2,1,3), =(-2-2)2+(1+1)2+(3-3)2 =(-4)2+(2)2+(0)2 =16+4 =20 =25
Therefore, the distance between the given two points is 25. Hence, the required value of k is 2.

About Miscellaneous Exercise Class 11 Chapter 12

Students often have a wrong notion that miscellaneous exercises are not important. But as mentioned before, they are very important to develop a student’s high order thinking skills. Miscellaneous Exercises Class 11 deals with the topics:

• Coordinate Axes and Coordinate Planes in Three Dimensional Space
• Coordinates of a Point in Space
• Distance between Two Points
• Section Formula

By solving these questions it becomes very easy for the students to attend all the types of questions in the main exam. Class 11 syllabus is the foundation for Class 12 subjects and is very important for competitive exams. By solving miscellaneous exercises, students can explore the subject well.

Chapter Description: Introduction to Three Dimensional Geometry

The chapter deals with 3-D geometry and 3-D figures. A lot of formulae have to be remembered by the students for scoring great scores. A few key points from the chapter are:

• A cartesian coordinate system in three dimensions is made up of three mutually perpendicular lines called the x, y, and z-axes. They are both measured in the same length unit.
• The three planes XY-plane, YZ-plane, and ZX-plane are defined by the axes of the coordinate planes, which are a pair of axes.
• The space is divided into eight sections by the three coordinate planes, which are known as octants.
• In three-dimensional geometry, the coordinates of a point P (x, y, z) are expressed as an ordered triplet. The distances between the YZ, ZX, and XY-planes are represented by x, y, and z.
• On the x-axis, any point is represented as (x, 0, 0)
• (0, y, 0) represents any point on the y-axis; (0, y, 0) represents any point on the z-axis.

Benefits of Embibe NCERT Solutions: Know the Advantages

There are numerous benefits of solving NCERT in-text questions and solutions for the students. NCERT questions can give the students a clear idea about each topic since topic-wise questions are available in the textbooks. Here are a few reasons why students can rely on Embibe’s NCERT solutions:

• The Embibe NCERT solutions available on the Embibe website follow the most recent CBSE criteria and are quite reliable for test preparation.
• All solutions have been created by education specialists with many years of experience in teaching or working in the sector.
• They convey concepts and solutions in a straightforward and easy-to-understand manner.
• The solutions are detailed and aid students in grasping the concepts both factually and practically.
• Embibe delivers the NCERT Solutions PDF for, and it is accessible to everyone without the need to spend a lot of money.
• The in-text questions from the CBSE Class 11 textbooks are included in Embibe’s NCERT Solutions.
• The in-text questions from the CBSE Class 11 textbooks are included in Embibe’s NCERT Solutions.
• Embibe’s Maths Class 11 NCERT Solutions assist students in successfully and comprehensively preparing for competitive exams.
• Embibe NCERT solutions use a step-by-step method that allows students to understand problems and even acquire new techniques for solving them.
• Students can also obtain assistance with their homework and effectively prepare for the upcoming CBSE Class 11 test.
• It includes thorough solutions to all of the answers in the NCERT Maths Class 11 book, ensuring that no questions are left unanswered.
• Long answer, short answer, MCQs, and other problems are included in the Embibe NCERT solutions, which aid students in their test preparation.

FAQs on Miscellaneous Exercise Chapter 12 Class 11

Students might face a lot of challenges while preparing for the Class 11 exams. This is because each and every concept might require a lot of time to understand. However, we have provided a few frequently asked questions related to the topic along with their solutions.

Q.1. Where can I download the miscellaneous exercise of introduction to 3D Geometry?
Ans: All the exercises of Chapter 12 Maths Class 11 can be downloaded from Embibe. Embibe provides the accurate answer key for each exercise that is given by the subject experts. Also, students can practice the questions for and access the study materials as well. There are mock tests, video lessons, and feedback sessions given by Embibe for the students of cost! So, the exercises along with the miscellaneous exercises Maths is given and can be downloaded from Embibe.

Q.2. What are the few important topics under introduction to 3D geometry?
Ans: A few of the important topics are the study of points, lines, and solid shapes in three-dimensional coordinate systems are known as trigonometry. It will teach students how to use the z-coordinate in conjunction with the x and y coordinates to calculate the exact location of a point in the 3D coordinate plane. It is a fundamental theory with applications in different fields of science and higher mathematics. The concept of trigonometric ratios is useful in 3D geometry.

Q.3. How many exercises are there in chapter three dimensional geometry class 11?
Ans: Miscellaneous exercises deal with all the topics. Given below are the exercise titles and the topics they deal with:

Section Name	Topic Name
12.1	Introduction
12.2	Co-Ordinate Axes and Co-ordinate Planes in Three Dimensional Space
12.3	Coordinate of a Point in Space
12.4	Distance Between Two Points
12.5	Section Formula

Q.4. What are the ways I can prepare for Class 11 exams?
Ans: One of the most difficult academic years is Class 11. For the first time, pupils are confronted with a detailed curriculum covering a wide range of disciplines. The complexity of the course first overwhelms many students. However, their desire to be an engineer or a doctor causes them to feel conflicted. Students must extensively study their Class 11 textbooks and obtain a comprehensive knowledge of the material. This will not only help kids do well in their board examinations but also in competitive exams. Students should start with NCERT example Class 11 to improve their conceptual foundation before moving on to reference books like those by RD Sharma or HC Verma. As applicants, even practicing from the previous year’s Class 11 question paper is beneficial.

Q.5. Is the chapter introduction to 3D Geometry easy?
Ans: Yes! The chapter despite many formulae, if students are thorough with the concepts, can score great scores! It is often fun to learn about geometrical figures and their dimensions. Some of the practice questions are:
1. If a line L creates angles of 135°, 90°, and 45° with the x, y, and z-axes, find the direction cosines.
2. Show that A(5, 8, 7), B (-1, -2, 1), and C(2, 3, 4) are collinear.
3. If the vertices of a triangle have the coordinates (-1, 1, 2), (3, 5, -4), and (-5, -5, -2). Find the direction of the sides’ cosines.
4. Find the vector equation for the line L that passes through (3, 4, 6) and (-1, 0, 2).

Attempt 12th CBSE Exam Mock Tests

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We hope that the article will help you in resolving all your doubts. If any doubts persist, feel to contact us and we will get back to you at the earliest!