NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

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

Class-12-Mathematics-Solutions-Chapter-11 pdf

 

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:

11.1 Introduction

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 Plane

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.

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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.

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