Subject specialists have created NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry, which includes thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Solutions for Class 12 provide useful solutions for improving conceptual knowledge.
The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Solutions for Class12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12pupils perform well in upcoming competitive exams.
The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.
| Exercise 11.1 solutions |
| Exercise 11.2 solutions |
| Exercise 11.3 solutions |
| Miscellaneous Exercise solutions |
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry
The topics and subtopics covered in Chapter 11- Three Dimensional Geometry of NCERT Solutions for Class 12 are as follows:
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- Three Dimensional Geometry
According to the new CBSE Syllabus 2021-22, the chapter Three Dimensional Geometry is part of the unit Vectors and Three–Dimensional Geometry in term II. It 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 Solutions 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 l, m, n are the direction cosines of a line, then l^2+m^2+n^2 = 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 other from any point (ideally through the origin).
- If l1 , m1, n1 and l2, m2, n2 are the direction cosines of two lines; and θ is the acute angle between the two lines; then cosθ = |l1l2 + m1m2 + n1n2|
These are some of the topics covered in the three-dimensional geometry chapter. NCERT Solutions for Class 12 Maths Chapter 11 can be used as a quick reference to help students understand complicated concepts. Refer to the NCERT Textbook and NCERT Solutions of Class 12 Maths for further information on the chapter.
Key Features of NCERT Solutions for Class 12 Maths Chapter 11- Three Dimensional Geometry
Students who study Class 12 Three Dimensional Geometry utilizing the NCERT Solutions 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.
Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 11
- What is three-dimensional geometry in NCERT Solutions for Class 12 Maths Chapter 11?
- What are the important topics covered in Chapter 11 of NCERT Solutions for Class 12 Maths?
- Is NCERT Solutions for Class 12 Maths Chapter 11 the best study material for the students during revision?
1. What is three-dimensional geometry in NCERT Solutions for Class 12 Maths Chapter 11?
It is an area of mathematics that deals with three-dimensional coordinate systems and the study of lines, points, and solid objects. It will teach students how to use the z-coordinate in conjunction with the x and y coordinates to identify the precise location of a point in three-dimensional coordinate planes.
2. What are the important topics covered in Chapter 11 of NCERT Solutions for Class 12 Maths?
The topics and subtopics covered in NCERT Solutions for Class 12 Maths Chapter 11 are listed below:
11.1 Introduction
11.2 Direction Cosines and Direction Ratios of a Line
11.3 Equation of a Line in Space
11.4 Angle between Two Lines
11.5 Shortest Distance between Two Lines
11.6 Plane
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
3. Is NCERT Solutions for Class 12 Maths Chapter 11 the best study material for the students during revision?
Yes, the NCERT Solutions for Class 12 Maths Chapter 11 is the finest study material for students who want to easily revise complicated ideas. Each solution includes a reasonable explanation to assist pupils in learning. INFINITY LEARN’s in-house team of professionals has framed the step-by-step answers to encourage students to think analytically. These solutions can also be compared to obtain an idea of what different options are available for solving textbook problems.
