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Edited By Ramraj Saini | Updated on Mar 22, 2022 05:25 PM IST

NCERT Class 11 Maths chapter 12 notes based on Pair of Linear Equations we will study parallel lines, coinciding lines, and intersecting lines. The chapter Three Dimensional Geometry Class 11 notes also includes how to draw a line in a plane.

Introductory Part may include: The NCERT Class 11 chapter 12 notes Revisiting based on Pair of Linear Equations we will study parallel line, coinciding line and intersecting line of Three Dimensional Geometry 11 notes. CBSE Cass 11 Maths chapter 12 notes and Class 11 Maths chapter 12 notes include the basic equations in the chapter. These topics can also be downloaded from class 11 Maths chapter 12 notes pdf download.

**JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | **

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**Also, students can refer,**

- NCERT Solutions for Class 11 Maths Chapter 12 Introduction To Three Dimensional Geometry
- NCERT Exemplar Class 11 Maths Chapter 12 Introduction To Three Dimensional Geometry

**Distance Formula**

Suppose that there are two points (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}) then the distance formula is given as

**Section Formulas**

Suppose that there are two points (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}) are divided into m:n.

Then section formula is given as:

**Systems Of Planes**

An equation of a plane contains three independent constants, as such a plane is uniquely determined by three independent conditions. If we consider a plane satisfying just two given conditions, its equation will contain one arbitrary constant. If we consider a plane satisfying one given condition, its equation will contain two arbitrary constants.

We give below the equations of some well-known systems of planes:

The equation ax + by + cz + k = 0 represents a system of planes parallel to the plane ax + by + cz + d = 0 d, k are parameters.

The equation ax + by + cz + k = 0 represents a system of planes perpendicular to the line x/a = y/b = z/c .

The equation a_{1}x + b_{1}y + c_{1}z + d_{1} = 0 + λ(a_{2}x + b_{2}y + c_{2}z + d_{2} )= 0 a system of planes passing through the intersection of the planes are a_{1}x + b_{1}y + c_{1}z + d_{1} = 0 and a_{2}x + b_{2}y + c_{2}z + d_{2} = 0.

where λ is a parameter.

**Angle Between Two Planes**

Let there are two planes a_{1}x + b_{1}y + c_{1}z + d_{1} = 0 and a_{2}x + b_{2}y + c_{2}z + d_{2} = 0

Then the angle between is given as

**The Symmetrical Form Of The Equation Of A Line**

If a straight line passes through a given point (x_{1},y_{1},z_{1}) and has direction cosines l, m, n, then the coordinates of any point on it satisfy the equations

**Vector Equations:**

Parametric vector equation of the line through a point with position vector a and parallel to the vector b is

where λ is a scalar parameter.

Three-Dimensional Geometry Class 11 notes is helpful to revise the chapter and to understand the main topics covered in the chapter. NCERT Class 11 Maths chapter 12 and Class 11 Three Dimensional Geometry include the main topics of Class 11 CBSE Maths Syllabus. CBSE Class 11 Maths chapter 12 notes and Three Dimensional Geometry Class 11 Notes highlights the main syllabus. Three-Dimensional Geometry Class 11 notes pdf download can be used to prepare in offline mode.

NCERT Class 11 Maths Chapter 12 Notes |

- NCERT Exemplar Class 11 Solutions
- NCERT Exemplar Class 11 Maths
- NCERT Exemplar Class 11 Physics
- NCERT Exemplar Class 11 Chemistry
- NCERT Exemplar Class 11 Biology

- NCERT Solutions for Class 11 Mathematics
- NCERT Solutions for Class 11 Chemistry
- NCERT Solutions for Class 11 Physics

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