The NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry are offered here to assist students in understanding how to tackle various questions. Everything in the real world has a three-dimensional shape, as we can see by looking around. You will understand Three-Dimensional Geometry in-depth in this chapter.
- All you need to know about NCERT Solutions Class 12 Maths
You can easily get full marks in this chapter’s questions by practicing all of the questions in the NCERT Class 12 Maths textbook. Hence, Download the 12th Maths NCERT Solutions PDF for a quick peek at the content of your Maths syllabus.
Download NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry PDF
The NCERT Solutions for Three Dimensional Geometry in Class 12 are easy to grasp. These solutions include all of the exercise questions in the book and are up to date with CBSE guidelines. The NCERT Solutions for Class 12 Maths Chapter 11 are provided in PDF format, which may be downloaded and viewed below:
Three Dimensional Geometry Class 12 NCERT Solutions PDF Download
What will you get in Three Dimensional Geometry Class 12 NCERT Solutions PDF?
The Math topics addressed in NCERT Solutions for Class 12 Chapter 11- Three Dimensional Geometry entail:
11.2 Direction Cosines and Direction Ratios of a Line
11.2.1 Relation between the direction cosines of a line
11.2.2 Direction cosines of a line passing through two points
11.3 Equation of a Line in Space
11.3.1 Equation of a line through a given point and parallel to a given vector b.
11.3.2 Equation of a line passing through two given points
11.4 Angle between Two Lines
11.5 Shortest Distance between Two Lines
11.5.1 Distance between two skew lines
11.5.2 Distance between parallel lines
11.6.1 Equation of a plane in normal form
11.6.2 Equation of a plane perpendicular to a given vector, passing through a given point
11.6.3 Equation of a plane passing through three non-collinear points
11.6.4 Intercept form of the equation of a plane
11.6.5 Plane passing through the intersection of two given planes
11.7 Coplanarity of Two Lines
11.8 Angle between Two Planes
11.9 Distance of a Point from a Plane
11.10 Angle between a Line and a Plane
NCERT Solutions for Class 12 Maths Chapter 11 Exercises include:
- Exercise 11.1 – 5 Questions (Short Questions)
- Exercise 11.2 – 17 Questions (9 Short Questions and 8 Long Questions)
- Exercise 11.3 – 14 Questions (5 Short Questions and 9 Long Questions)
Important Topics in NCERT Solutions for Class 12 Maths Chapter 11
The following are some of the topics covered in NCERT Solutions for Class 12 Maths Chapter 11:
- Direction cosines and Direction Ratios – How to find using different methods – when the angle is given, when a side is given, when two points are given
- Equation of Line – We form an equation of a line in different cases – one point and 1 parallel line, 2 points given. We also learn how to convert the vector form of the equation to Cartesian form
- Angle between two lines – We find Angle between two lines using Vector formula, Cartesian Formula, Using Direction Cosines and Ratios
- Shortest Distance between two lines – Finding the shortest distance between two parallel and two skew lines
- Equation of plane – Finding the equation of a plane in normal form, when perpendicular and point passing through is given, when passing through 3 Non-Collinear Points. We also find the equation of plane using intercept form, and when a plane is passing through the intersection of planes
- Coplanarity of 2 Lines – Checking if 2 lines are coplanar
- Angle between two planes – Finding angle between two planes using Vector and Cartesian method
- Distance between point and plane – Both Vector and Cartesian Formula
- Angle between Line and Plane – Vector formula only
- Equation of line under planes condition – Finding Equation of line when some condition between two planes is given.
- Point with Lines and Planes – Finding coordinates of a point when the line crosses through a plane or Finding a point where line and plane intersect.
Advantages of Three Dimensional Geometry Class 12 NCERT Solutions
Let’s check out few benefits of solving Three Dimensional Geometry Class 12 NCERT Solutions:
- This solution, designed by experienced professionals and subject specialists, is fully researched and carefully organized to include a detailed solution to every question in the NCERT Chapter 11 textbooks.
- It aids you in determining the gaps between the paper framed and the course topic.
- It also aids in the preparation of undergraduate and graduate-level competitive exams such as IIT JEE, BITSAT, NEET, and so on.
- Content is well-structured.
- These solutions are supported by appropriate explanations and examples.
Well, we have jotted down the CBSE NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry in here. Also, if you are facing any doubts regarding the same, make sure to comment down so that our professional may reach out to you.
FAQs: NCERT Solutions for Class 12 Maths Chapter 11
How many questions were there in exercise 11.1 of chapter 11 Maths class 12?
There are a total of 5 questions in exercise 11.1 of chapter 11 Maths class 12.
Are Class 12 Maths NCERT solutions Ch 11 important to study?
Yes. Chapter 11 Class 12 Maths is important to study for 12th board preparation.
Can I get an overview of the Ch 11 Maths Class 12 Solutions exercises?
Yes. You can receive an overview of the NCERT Solutions for Class 12 Maths Chapter 11 exercises from the above blog.
Can I get a perfect score on the NCERT Solutions for Chapter 11 Maths Class 12?
Yes. KopyKitab’s experts created the NCERT Solutions for Class 12 Maths Chapter 11 after performing extensive research on each term. It will help you to score 100 in Class 12 Maths.
How many exercises are there in Chapter 11 of the NCERT textbook for Class 12 Maths?
In total, there are 3 exercises in Chapter 11 Class 12 Maths.
Where can I download Maths Chapter 11 Class 12 NCERT solutions?
You can download NCERT Solutions for Class 12 Maths Chapter 11 from the above blog.
Are NCERT Solutions for Class 12th Maths sufficient for Chapter 11 preparation?
Yes. NCERT Solutions for Class 12 Maths is sufficient for Chapter 11 preparation.