NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry PDF – is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT Solutions for Class 12 Maths Chapter 11 play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.
CBSE NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.
NCERT Solutions for Class 12 Maths Chapter 11
The topics and sub-topics included in the Three Dimensional Geometry chapter are the following:
Exercise 11.1: Introduction
Exercise 11.2: Direction Cosines and Direction Ratios of a Line
Exercise 11.2.1: Relation between the direction cosines of a line
Exercise 11.2.2: Direction cosines of a line passing through two points
Exercise 11.3: Equation of a Line in Space
Exercise 11.3.1: Equation of a line through a given point and parallel to a given vector b.
Exercise 11.3.2: Equation of a line passing through two given points
Exercise 11.4: Angle between Two Lines
Exercise 11.5: Shortest Distance between Two Lines
Exercise 11.5.1: Distance between two skew lines
Exercise 11.5.2: Distance between parallel lines
Exercise 11.6: Plane
Exercise 11.6.1: Equation of a plane in normal form
Exercise 11.6.2: Equation of a plane perpendicular to a given vector, passing through a given point
Exercise 11.6.3: Equation of a plane passing through three non-collinear points
Exercise 11.6.4: Intercept form of the equation of a plane
Exercise 11.6.5: Plane passing through the intersection of two given planes
Exercise 11.7: Coplanarity of Two Lines
Exercise 11.8: Angle between Two Planes
Exercise 11.9: Distance of a Point from a Plane
Exercise 11.10: Angle between a Line and a Plane
CBSE NCERT Solutions For Class 12 Maths Chapter 11 PDF Download
Candidates can download the NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry PDF for free study in offline mode. All the solutions provided on this page are solved by top academic experts of Embibe in order to help students in their studies.
NCERT Solutions For Class 12 Maths Chapter 11 – Three Dimensional Geometry NCERT Solutions
In Class XI, while studying Analytical Geometry in two dimensions, and the introduction to three-dimensional geometry, we confined to the Cartesian methods only. In the previous chapter of this book, we have studied some basic concepts of vectors. We will now use vector algebra to three-dimensional geometry. The purpose of this approach to 3-dimensional geometry is that it makes the study simple and elegant.
In this chapter, we shall study the direction cosines and direction ratios of a line joining two points and also discuss about the equations of lines and planes in space under different conditions, angle between two lines, two planes, a line and a plane, shortest distance between two skew lines and distance of a point from a plane. Most of the above results are obtained in vector form. Nevertheless, we shall also translate these results in the Cartesian form which, at times, presents a more clear geometric and analytic picture of the situation.
FAQs Related to NCERT Solutions for Class 12 Maths Chapter 11 PDF
Q. Where can I get NCERT Solutions for Class 12 Maths PDF to download for all chapters?
A. Follow the link NCERT Solutions for Class 12 Maths to download for all chapters PDF on Embibe.
Q. What is the name of CBSE NCERT Solutions for Class 12 Maths Chapter 11?
A. Class 12 Maths Chapter 11 name is Three Dimensional Geometry.
Q. How many exercises are there in NCERT Solutions for Class 12 Maths Chapter 11 PDF?
A. There is a total of 10 exercises with subtopics. in Class 12 Maths Chapter 11.
Q. What is the formula for the angle between two lines of Class 12 Maths?
A. If one of the line is parallel to y-axis then the angle between two straight lines is given by tan θ = ±1/m where ‘m’ is the slope of the other straight line. If the two lines are a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, then the formula becomes tan θ = |(a1b2 – b1a2)/(a1a2 + b1b2)|
Q. How do you calculate a plane class 12 Maths?
A. We get the point-normal equation A(x−a)+B(y−b)+C(z−c) = 0. for a plane. for the equation of a plane having normal n=⟨A,B,C⟩. Here D=n⋅b=Aa+Bb+Cc.
Embibe provides CBSE study material that covers the whole CBSE Class 12 syllabus for Maths. You can also solve Maths practice questions for every chapter in the CBSE Class 12 syllabus for Maths that will also help you in your preparation of JEE as well.
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