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# NCERT Solutions for Class 12 Maths Chapter 11 Free PDF Download

## 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

The 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.

### CBSE Class 12 Maths Chapter 11 – 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. 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 – 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.

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