**NCERT Solutions for Class 12 Maths Chapter 11 – ****Three Dimensional Geometry**

The NCERT solutions for class 12 maths chapter 11 cover the solutions for all the exercise problems of the textbook. These solutions are as per the NCERT guidelines and syllabus

TheÂ NCERT solutions for class 12 maths chapter 11 are prepared by experts by our expert faculties which breaks down into detailed steps. NCERT solutions cover all the concept, help you in scoring higher marks.

Toppr provides free study materials, last 10 years of question papers, 1000+ hours of video lectures for free. Download Toppr app forÂ AndroidÂ andÂ iOSÂ orÂ SignupÂ for free.

DownloadÂ NCERT Solutions for other subjects here.

DownloadÂ NCERT Solutions for Class 12 here.

DownloadÂ NCERT Solutions for Class 12 Maths Chapter-wise here.

**CBSE Class 12 Maths Chapter 11 â€“ ****Three Dimensional Geometry NCERT Solutions**

In NCERT solutions for class 12 maths chapter 11, you will study about the direction cosines and direction ratios, cartesian and vector equation, coplanar and skew lines, shortest distance between two lines, cartesian and vector equation of a plane, the distance of a point from a plane.

**Sub-topics covered under NCERT Solutions for Class 12 Maths Chapter 11**

- 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**

In NCERT solutions for class 12 maths chapter 11, you will learn direction cosines and ratios of a line, cartesian and vector equation, coplanar and skew lines.Â Let us now discuss the subtopics include in NCERT solutions for class 12 maths chapter 11.

**11.1- Introduction**

In this, you use vector algebra to three-dimensional geometry.

**11.2 – Direction Cosines and Direction Ratios of a Line**

In this, you study the direction of angles of the cosine of line.

**11.2.1- Relation between the direction cosines of a line**

In this, you study the relationship between the direction of cosine.

**11.2.2 – Direction cosines of a line passing through two points**

In this, you will study to find the direction of the cosine of the line passing through 2 points.

**11.3 – Equation of a Line in Space**

In this, you will study the vector and cartesian equations of a line in space.

**11.3.1- Equation of a line through a given point and parallel to a given vector b**

In this, you will study to find the vector equation of a line.

**11.3.2 – Equation of a line passing through two given points**

In this, you will study to find the position of the vector by the equation of the line passing through it.

**11.4 – Angle between Two Lines**

In this, you will study about the angles between 2 vectors.

**11.5 – Shortest Distance between Two Lines**

In this, you will study to find the distance between two lines.

**11.5.1- Distance between two skew lines**

In this, you will study to find the distance between two non-intersecting lines but not parallel.

**11.5.2 – Distance between parallel lines**

Here method to find the distance between the two parallel lines is explained

**11.6 â€“ Plane**

In this topic, the plane is explained.

**11.6.1- Equation of a plane in normal form**

In this, you will find the equation of a plane.

**11.6.2 – Equation of a plane perpendicular to a given vector, passing through a given point**

In this, you will find the vector equation of the perpendicular plane.

**11.6.3 – Equation of a plane passing through three non-collinear points**

In this, you will find the vector equation of the plane passing through non-collinear points.

**11.6.4 – Intercept form of the equation of a plane**

This explains the intercept form.

**11.6.5 – Plane passing through the intersection of two given planes**

This gives the vector equation of the intersection plane.

**11.7 – Coplanarity of Two Lines**

This explains Coplanarity.

**11.8 – Angle between Two Planes**

In this, you will find the angle between two planes.

**11.9 – Distance of a Point from a Plane**

This explains to find the distance of a point from the plane.

**11.10 – Angle between a Line and a Plane**

This explains to find the angle between line and plane.

**You can download NCERT Solutions for Class 12 Maths Chapter 11 for free by clicking on the download button below**

**Download Toppr – Best Learning App for Class 5 to 12**

With Toppr App, you get free pdf downloads of study material, free videos and free doubt solving sessions, free online tests. Download Toppr app forÂ AndroidÂ andÂ iOSÂ orÂ SignupÂ for free.

## Leave a Reply