Chapter 11:

NCERT Books Free Download for Class 12 Maths Chapter-11 Three Dimensional Geometry

NCERT Books for Class 12 Maths Chapter-11 Three Dimensional Geometry Free PDF Download

Everything in the real world has a three-dimensional shape, as we can see by looking around and touching. Students learn about Three-Dimensional Geometry in-depth in this chapter. By answering all of the questions in the NCERT textbook, students can easily achieve full marks in the questions from this chapter. Chapter Three Dimensional Geometry is simple to comprehend.

More Free Study Material for Three - Dimensional Geometry

Ncert solutions

Revision notes

Important questions

NCERT Books for Class 12 Maths Chapter 11- Three Dimensional Geometry Highlights

Students who study Chapter 11- Three Dimensional Geometry Utilising the NCERT Books Will be Able to Comprehend the Following:

A line connecting two places has direction cosines and direction ratios.
The shortest distance between two lines, coplanar and skew lines, and the Cartesian equation and vector equation of a line.
A plane's Cartesian and vector equations.
The angle is formed by two lines, two planes, or a line and a plane.
A point's distance from a plane.

Important Questions From Previous Years

Find the Cartesian and Vector equations for the line that goes through the point (-2, 4, -5) and is parallel to (x+3)/3 = (y-4)/5 = (8-z)/-6. (2017 CBSE Sample Paper)
Find the vector equation of the line parallel to the line 5x – 25 = 14 – 7y = 35z and pass-through point A(1, 2, –1). (Delhi, India, 2017)
The centroid of triangle ABC is the point (α, β, γ) where a plane intersects the coordinate axes in A, B, and C. Show that the plane's equation is x/α + y/β + z/γ = 3. (2017 CBSE Sample Paper)
If the vectors p = ai + j + k, q = I + bj + k, and r = I + j + ck are all coplanar, then 1/(1-a) + 1/(1-b) + 1/(1-c) = 1 for a, b, and c ≠ 1. (2017 CBSE Sample Paper)

Topics Covered By the Chapter Three Dimensional Geometry

According to the current CBSE Syllabus 2024-25, the chapter Three Dimensional Geometry accounts for 14 of the total marks. This chapter includes three activities, as well as a random, practice to assist students to grasp the fundamentals of Three Dimensional Geometry. The following are some of the topics covered in Chapter 11 of NCERT Books for Class 12 Maths:

The cosines of the angles formed by a line with the positive directions of the coordinate axes are called the direction cosines of a line.
If a line's direction cosines are l, m, and n, then l² + m² + n² = 1.
A line's direction ratios are the numbers that are proportional to the line's direction cosines.
Skewed lines are lines that are neither parallel nor intersecting in space. They are positioned on distinct planes.
The angle between skew lines is the angle formed by two intersecting lines drawn parallel to one another from any point (ideally through the origin).
If l₁, m₁, n₁, and l₂, m₂, n₂ are the direction cosines of two lines, and is the acute angle between them, cos = |l₁l₂ + m₁m₂ + n₁n₂|

FAQs on NCERT Books Free Download for Class 12 Maths Chapter-11 Three Dimensional Geometry

1. What is the significance of the Chapter 11 Three Dimensional Geometry of NCERT Class 12 Maths Book?

The NCERT Class 12 Maths Book's Chapter 11 Three Dimensional Geometry is created by experts to offer a thorough understanding of all fundamentals. These are provided by Vedantu for free on its official website(vedantu) and mobile app. Students will be able to achieve full conceptual knowledge and perform well in tests if they strategically prepare all of the important topics. The well-crafted format of the exercises in NCERT is ideal for encouraging arithmetic study.

2. Is it necessary for me to go over all of the questions in Chapter 11 Three Dimensional Geometry of NCERT Class 12 Maths Book?

When you practise all of the questions in Chapter 11 Three Dimensional Geometry of NCERT Class 12 Maths Book you will have a step-by-step understanding of each topic. The questions in these solutions are well-placed at a progressively increasing level, allowing students to adjust to the increasing difficulty with ease. By solving all of these sums, children may quickly acquire the key foundations of three-dimensional geometry. These solutions are also useful for preparation for numerous competitive exams and higher-level studies.

3. What are the important topics covered in Chapter 11 of the NCERT Class 12 Maths Book, Three Dimensional Geometry?

Chapter 11 of Class 12 Maths, Three Dimensional Geometry, concisely explains all of the important principles of three-dimensional geometry. Direction cosines, direction ratios of a line joining two points, cartesian equation of a line, vector equation of a line, coplanar lines, skew lines, the shortest distance between two lines, cartesian and vector equation of a plane are some of the important topics covered in NCERT Class 12 Maths Book Chapter 11 Three Dimensional Geometry. The goal of curating these answers is to help kids realise their potential in Maths and achieve their goals.

4. What are the key formulae in Chapter 11 of the NCERT Class 12 Maths Book, Three Dimensional Geometry?

The NCERT Class 12 Maths Book's Chapter 11 Three Dimensional Geometry primarily focuses on imparting knowledge of various methods for determining the direction of cosines and ratios. Apart from that, these resources aid in the understanding of a line's Cartesian and vector equations. With the use of examples and drawings, these topics are thoroughly explained. It is advisable to go through the Maths books thoroughly in order to select and practice the key formulas in Chapter 11.