Introduction To Three Dimensional Geometry Class 11th Notes - Free NCERT Class 11 Maths Chapter 12 notes - Download PDF

# Introduction To Three Dimensional Geometry Class 11th Notes - Free NCERT Class 11 Maths Chapter 12 notes - Download PDF

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.

Also, students can refer,

## Pair Of Linear Equations In Two Variables Class 11 Notes

Distance Formula

Suppose that there are two points (x1,y1,z1) and (x2,y2,z2) then the distance formula is given as

Section Formulas

Suppose that there are two points (x1,y1,z1) and (x2,y2,z2) 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 a1x + b1y + c1z + d1 = 0 + λ(a2x + b2y + c2z + d2 )= 0 a system of planes passing through the intersection of the planes are a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0.

where λ is a parameter.

Angle Between Two Planes

Let there are two planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 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 (x1,y1,z1) 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.

## Significance of NCERT Class 11 Maths Chapter 12 Notes

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 Notes Chapter Wise.

 NCERT Class 11 Maths Chapter 1 Notes NCERT Class 11 Maths Chapter 2 Notes NCERT Class 11 Maths Chapter 3 Notes NCERT Class 11 Maths Chapter 4 Notes NCERT Class 11 Maths Chapter 5 Notes NCERT Class 11 Maths Chapter 6 Notes NCERT Class 11 Maths Chapter 7 Notes NCERT Class 11 Maths Chapter 8 Notes NCERT Class 11 Maths Chapter 9 Notes NCERT Class 11 Maths Chapter 10 Notes NCERT Class 11 Maths Chapter 11 Notes NCERT Class 11 Maths Chapter 12 Notes NCERT Class 11 Maths Chapter 13 Notes NCERT Class 11 Maths Chapter 14 Notes NCERT Class 11 Maths Chapter 15 Notes NCERT Class 11 Maths Chapter 16 Notes

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Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?

 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9