## Class 12 Maths Notes Of All Chapters Pdf Download

Table of Contents

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Mathematics is the most important subject in class 12. It is a compulsory subject and is taught from class 1 to 10. Mathematics not only helps you in your career but also builds a strong foundation for your future.

The objective of this article is to provide you with some useful class 11 maths notes that will help you solve problems and clear your doubts.

Mathematics is an important subject in class 12. It is the base of all subjects and it has a great scope for the future. The notes of class 12 helps the students to understand the concepts in a better way.

The 12th class math notes are written by experienced teachers with years of teaching experience and knowledge of the subject. They help students to understand the concepts with examples and illustrations.

**Content Type For Math Notes for class **12

- Definitions
- Examples
- Exercises
- MCQs

The above paragraph shows the information about definition, example, exercises and MCQs which makes it easy to understand the notes of **math 12 class notes chapter **wise.

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## About Class 12 Maths Notes

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The following are some of the topics that we will cover of 12th class math notes:

## Important Topics Of Math For Class 12

Chapter 1: Functions and Limits

Introduction

Introduction to Function

More on Introduction to Functions

Domain & Range of Binary Relation

Graphs of Algebraic Functions

Graph of Functions Defined Piecewise

Types of Functions (Practice Test)

Algebraic Functions

Trigonometric Functions

Introduction to Binary Operations

More on Inverse Trigonometric Functions

Further to Inverse Trigonometric Functions

Operations on Residue Classes Modulo n

Properties of Binary Operations

More on Logarithmic Functions

Hyperbolic Functions

Inverse Hyperbolic Functions

Explicit and Implicit Functions

Parametric Functions

Even and Odd Functions

Problem-Even and Odd Functions

Composition of Function and Inverse of a Function (Practice Test)

Composition of a Functions

Problem-Composition of Functions

Inverse of a Function

More on Inverse of a Functions

Problem-Inverse of a Function

Algebraic Method to find the Inverse Function

Problem-Algebraic Method to find the Inverse Function

Limit of a Function and Theorems on Limits

Meaning of the Phrase ‘x’ Approaches zero, Infinity

Problem-Meaning of the Phrase ‘x’ Approaches zero, Infinity

Concept of a Limit of a Function

Problem-Concept of Limit of a Function

Limits of Important Functions

Limit at Infinity

Method for Evaluating the Limits at Infinity

Problem-Method for Evaluating the Limits at Infinity

Deducting Formulae at Limit Approaches to 0 and infinity

Problem-Deducting Formulae at Limit Approaches to 0 and infinity

The Sandwich Theorem

Continuous and Discontinuous Functions

One-Sided Limits

Criterion for Existence of Limit of a Function

Problem1-Criterion for Existence of Limit of a Function

Continuity of a Function at a Number

Graphs

Graph of the Exponential Function

Problem1-Graph of the Exponential Function

More on Graph of Exponential Function

Problem1-More on Graph of Exponential Function

Graph of Common Logarithmic Function

Problem1-Graph of Common Logarithmic Function

Graph of Natural Logarithmic Function

Problem1-Graph of Natural Logarithmic Function

Graphs of Implicit Functions-Circle

Problem1-Graphs of Implicit Functions-Circle

Graphs of Implicit Functions-Ellipse

Graph of Parametric Equations

Problem1-Graph of Parametric Equations

Graphs of Discontinuous Functions

Problem1-Graphs of Discontinuous Functions

Graphical Solution of the Equation

Chapter 2: Differentiation

2.1: Introduction (Practice Test)

Introducing Dependent and Independent Variables

Average Rate of Change

Derivative of a Function

More on Derivative of a Function

Notation for Derivative

Geometrical Interpretation of a Derivative

More on Geometrical Interpretation of Derivative

2.2: Finding f'(x) from Definition of Derivative (Practice Test)

Derivative by First Principle

More on Derivative by First Principle

Problem1-Derivative by First Principle

Problem2-Derivative by First Principle

2.3: Theorems on Definition

Derivative of a Constant Function

Power Rule for Differentiation

Problem1-Power Rule for Differentiation

Derivative of a sum or Difference of Functions

Problem1-Derivative of a sum or Difference of Functions

Derivative of Product

Problem1-Derivative of Product

Derivative of a Quotient

More on Derivative of a Quotient

2.4: The Chain Rule (Practice Test)

Differentiation by Chain Rule

More on Differentiation by Chain Rule

Problem1-Differentiation by Chain Rule

Problem2-Differentiation by Chain Rule

2.5: Derivative of Inverse Functions

Derivative of Inverse Functions

2.6: Derivative of Functions Given in the Form of Parametric Equations

Derivative of Parametric Equations

Problem1-Derivative of Parametric Equations

2.7: Differentiation of Implicit Relations

Implicit Differentiations

Problem-Implicit Differentiations

Problem-Implicit Differentiations

2.8: Derivatives of Trigonometric Functions (Practice Test)

Derivative of Trigonometric Functions

More on Derivative of Trigonometric Functions

More Stuff on Derivative of Trigonometric Functions

Trigonometric Functions

2.9: Derivatives of Inverse Trigonometric Functions (Practice Test)

Derivative of Inverse Trigonometric Functions

2.10: Derivative of Exponential Functions

Derivative of Exponential Functions

Problem1-Derivative of Exponential Functions

2.11: Derivative of Logarithmic Functions

Derivative of Logarithmic Functions

Problem1-Derivative of Logarithmic Functions

2.12: Logarithmic Differentiation

Problem Solving-Logarithmic Functions

2.13: Derivative of Hyperbolic Functions (Practice Test)

Derivative of Hyperbolic Functions

More on Derivative of Hyperbolic Functions

Problem1-Derivative of Hyperbolic Functions

2.14: Derivatives of the Inverse Hyperbolic Functions (Practice Test)

Derivatives of the Inverse Hyperbolic Functions

More on Derivatives of the Inverse Hyperbolic Functions

Problem1-Derivatives of the Inverse Hyperbolic Functions

2.15: Successive Differentiation Or Higher Derivatives (Practice Test)

Introducing Higher Order Differentiation

Problem1-Introducing Higher Order Differentiation

Problem2-Introducing Higher Order Differentiation

Problem3-Introducing Higher Order Differentiation

Problem4-Introducing Higher Order Differentiation

2.16: Series Expansion of Functions (Practice Test)

Introducing Maclaurin’s Theorem

More on Maclaurin’s Theorem

Problem1-Introducing Maclaurin’s Theorem

Problem2-Introducing Maclaurin’s Theorem

2.17: Taylor Series Expansion of Functions

Taylor’s Theorem

More on Taylor’s Theorem

Problem 1a-Taylor’s Theorem

Problem2-Taylor’s Theorem

2.18: Geometrical Interpretation of a Derivative

Geometrical Interpretation of a Derivative

Increasing and Decreasing Functions (Practice Test)

Increasing and Decreasing Functions

More on Increasing and Decreasing Functions

Problem1-Increasing and Decreasing Functions

Relative Extrema

Introducing Relative Extrema

Problem1-Introducing Relative Extrema

2.21: Critical Values of Critical Points (Practice Test)

Relative Maxima and Minima

Problem2-Relative Maxima and Minima

Critical Values and Critical Points

Point of Inflexion

Second Derivative Test and Concavity

More on Second Derivative Test and Concavity

Chapter 3: Integration

3.1: Introduction (Practice Test)

Antidifferentiation and Indefinite Integral

Differentials of Variables

Integral Language and Notation

Difference between Delta y and dy

Problem1-Difference between Delta y and dy

3.2: Integration as Antiderivative (Practice Test)

Theorems on Anti-derivative

To Integrate x Raise to Power n

Problem1-To Integrate x Raise to Power n

To Integrate Sine Functions

To Integrate Cosine Functions

To Integrate Secant Squared Functions

To Integrate secx.tanx

To Integrate Cosecant.Cotangent Functions

Integrating Exponential Functions

To Integrate 1 by x

To Integrate Tangent Functions

To Integrate Cotangent Functions

To Integrate Cosecant Functions

Integrating Power Functions with Given Derivatives

More on Integrating Power Functions with Given Derivatives

3.3: Integration By Method of Substitution

Integration by Substitution

3.4: Some Useful Substitutions (Practice Test)

Some Useful Substitutions in Integration

More on Some Useful Substitutions in Integration

Some More Useful Substitutions in Integration

3.5: Integration By Parts (Practice Test)

Integration by Parts

Integration by Parts of Trigonometric Functions

More on Integration by Parts of Trigonometric Functions

3.6: Integration Involving Partial Fractions (Practice Test)

Integrating Partial Fractions with Non-repeated Factors

Problem1-Integrating Partial Fractions with Non-repeated Factors

Problem 1a-Integrating Partial Fractions with Non-repeated Factors

More on Integrating Partial Fractions with Non-repeated Factors

Integrating Partial Fractions with repeated Linear Factors

Problem1-Integrating Partial Fractions with Non-repeated Linear Factor

Problem 1a-Integrating Partial Fractions with Non-repeated Linear Factor

More on Integrating Partial Fractions with repeated Factors

Integrating Partial Fractions with Non-Repeated Quadratic Factors

Problem1-Integrating Partial Fractions with Non-Repeated Quadratic Fa

Problem 1a-Integrating Partial Fractions with Non-Repeated Quadratic F

More on Integrating Partial Fractions with Non-Repeated Quadratic Fac

Further to Integrating Partial Fractions with Non-Repeated Quadratic

3.7: The Definite Integrals (Practice Test)

The Definite Integral

Problem1-The Definite Integral

Problem2-The Definite Integral

Problem 2a-The Definite Integral

Area Under the Curve

Problem1-Area Under the Curve

Problem2-Area Under the Curve

More on Area Under the Curve

Negative Area by Definite Integral

Symmetrical Area by Integration

Area Bounded by Two Curves by Integration

To Deal with Negative and Positive Areas in Integration

Area Bounded by Two Curves Above and Below x-axis

3.8: Applications of Definite Integrals (Practice Test)

Application of Definite Integral

More on Application of Definite Integral

Differential Equations

Introduction to Differential Equation

More on Introduction to Differential Equation

Classification of Differential Equation

More on Classification of Differential Equation

Solving First Order Differential Equation

More on Solving First Order Differential Equation

Problem-Solving First Order Differential Equation

Problem-Solving First Order Differential Equation

Solving First Order Differential Equation by Initial Conditions

P1-Solving First Order Differential Equation by Initial Conditions

P2-Solving First Order Differential Equation by Initial Conditions

P3-Solving First Order Differential Equation by Initial Conditions

Homogeneous Differential Equation

Differential Equation Reducible to Homogeneous Differential Equation

Differential Equation of Orthogonal Trajectories

More on Differential Equation of Orthogonal Trajectories

Application of Differential Equations

More on Application of Differential Equations

Chapter 4: Introduction to Analytic Geometry

4.1: Introduction (Practice Test)

Cartesian Coordinate System & Cartesian Plane

Derivation of Distance formula

Use of Distance formula

Problem 1: Use of Distance formula

Points Dividing the Join of Two Points in Given Ratio

More on Points Dividing Join of Two Points in Given Ratio

Problem 1a-Points Dividing the Join of Two Points in Given Ratio

Problem 1b-Points Dividing the Join of Two Points in Given Ratio

4.2: Translation and Rotation of Axes (Practice Test)

Translation of Axes

Problem1-Translation of Axes

Problem2-Translation of Axes

Rotation of Axes

Problem1-Rotation of Axes

Problem2-Rotation of Axes

4.3: Equations of Straight Lines (Practice Test)

Inclination of Line

Problem1-Inclination of Line

Slope or Gradient of a Line

Gradient of a Straight Line Joining Two Points

Slope of Collinear Line Segments

Slope of Parallel Lines

Problem-Slope of Parallel Lines

Problem2-Slope of Parallel Lines

Equations of a Straight Line

More on Equations of Straight Line

Problem-Equations of a Straight Line

Derivation of Slope Intercept form

Problem1-Derivation of Slope Intercept form

Deriving Point-slope Form of Equation of Straight Line

Problem1-Deriving Point-slope Form of Equation of Straight Line

Symmetric Form of Equation of Straight Line

Problem1-Symmetric Form of Equation of Straight Line

Two Point form of Equation of Straight Line

Problem1-Two Point form of Equation of Straight Line

Intercept Form of Equation of Straight Line

Problem1-Intercept Form of Equation of Straight Line

Normal Form of Equation of Straight Line

Problem1-Normal Form of Equation of Straight Line

How 2 Variable Linear Equation Represent Straight Line

Problem1-How 2 Variable Linear Equation Represent Straight Line

Transforming General Linear Equation to Standard Forms

Problem1-Transforming General Linear Equation to Standard Forms

Transforming General Equation to Slope Intercept Form

Problem1-Transforming General Equation to Slope Intercept Form

Transforming General Form of Equation to Intercept Form

Problem1-Transforming General Form of Equation to Intercept Form

Transforming General Form of Equation to Normal Form

Problem1-Transforming General Form of Equation to Normal Form

Transforming General Form of Equation to Point Slope Form

Problem1-Transforming General Form of Equation to Point Slope Form

Transforming General Form of Equation to Symmetric Form

Problem1-Transforming General Form of Equation to Symmetric Form

Position of Point with Respect to Line

More on Position of Point with Respect to Line

Problem1-Position of Point with Respect to Line

Two and Three Straight Lines (Practice Test)

Relationship between Two and Three Straight Lines

The Point of Intersection of Straight Lines

Problem1-The Point of Intersection of Straight Lines

Condition of Concurrency of Three Straight Lines

More on Condition of Concurrency of Three Straight Lines

Problem1-Condition of Concurrency of Three Straight Lines

Equation of Lines Through Point of Intersecting 2 Lines

Problem1-Equation of Lines Through Point of Intersecting 2 Lines

Condition that Altitudes of Triangle are Concurrent

Moreo on Condition that Altitudes of Triangle are Concurrent

Problem1-Condition that Altitudes of Triangle are Concurrent

Condition that Right Bisectors of Triangle are Concurrent

More on Condition that Right Bisectors of Triangle Concurrent

Problem1-Condition that Right Bisectors of Triangle are Concurrent

Distance of Point From Line

Problem1-Distance of Point From Line

Problem2-Distance of Point From Line

Problem1-Distance between Two Parallel Lines

Area of Triangular Region With Given Vertices

More on Area of Triangular Region With Given Vertices

Problem1-Area of Triangular Region With Given Vertices

4.5: Angles Between Two Lines (Practice Test)

Angle Between Two Lines

Problem1-Angle Between Two Lines

Problem2-Angle Between Two Lines

Equation of a Straight Line in Matrix Form

More on Equation of Straight Line in Matrix Form

Problem1-Equation of a Straight Line in Matrix Form

Problem2-Equation of a Straight Line in Matrix Form

4.6: Homogeneous Equations-Second Degree in2 Variables (Practice Test)

Homogeneous Equation of Second Degree in Two Variables

More on Homogeneous Equation of 2nd Degree in 2 Variables

Homogeneous Equation of Degree ‘n’

More on Homogeneous Equation of Degree ‘n’

Problem1-Homogeneous Equation of Degree ‘n’

Problem-Homogeneous Equation of Degree ‘n’

Problem2-More on Homogeneous Equation of Degree ‘n’

Problem3-Homogeneous Equation of Degree ‘n’

Condition For the Lines to be Coincident

More on Condition For the Lines to be Coincident

Chapter 5: Linear Inequalities and Linear Programming (29 videos) (Practice Test)

5.1: Introduction

Introduction to Linear Inequalities

5.2: Linear Inequalities (Practice Test)

More on Introducing Linear Inequalities

Problem1-Introduction to Linear Inequalities

Graphing of Linear Inequality in Two Variables

More on Graphing of Linear Inequality in Two Variables

Problem1-Graphing of Linear Inequality in Two Variables

Problem2-Graphing of Linear Inequality in Two Variables

5.3: Region Bounded By 2 or 3 Simultaneous Inequalities (Practice Test)

Graphing System of Inequalities

More on Graphing System of Inequalities

Problem1-Graphing System of Inequalities

5.4: Problem Constraints

Problem1-Introducing Problem Constraints in Inequality

P1a-More on Introducing Problem Constraints in Inequality

5.5: Feasible Solution Set (Practice Test)

Feasible Solution in Inequality

More on Feasible Solution in Inequality

Problem1-Feasible Solution in Inequality

Problem 1a-More on Feasible Solution in Inequality

5.6: Linear Programming

Linear Programming

5.7: Linear Programming Problems (Practice Test)

Procedure For Determining Optimal Solution

More on Procedure For Determining Optimal Solution

Problem Solving in Linear Programming

More on Problem Solving in Linear Programming

Problem1-Procedure For Determining Optimal Solution

Problem1-More on Procedure For Determining Optimal Solution

Problem2-Procedure For Determining Optimal Solution

Problem2-More on Procedure For Determining Optimal Solution

Problem3-Procedure For Determining Optimal Solution

Problem3-More on Procedure For Determining Optimal Solution

Problem4-Procedure For Determining Optimal Solution

Problem4-More on Procedure For Determining Optimal Solution

Chapter 6: Conic Section

6.1: Introduction

Introduction to Conic Section

More on Introduction to Conic Section

Standard Form of Equation of Circle

General Form of Equation of Circle

More on General Form of Equation of Circle

Equation of Circle Passing Through Three Noncollinear Points

More on Equation of Circle Passing Through 3 Non-Collinear Points

Equation of Circle Passing Through 2 Points and its Centre onLine

Equation-Circle Passing Through 2 Points with 1 Tangential Point

Equation-Circle Passing Through 2 Points with 1 Tangential Point-1

Equation-Circle Passing Through 2 Points and Line

Equation-Circle Passing Through 2 Points and Line

6.2: Tangents and Normals

Equation of Tangent to Circle

More on Equation of Tangent to Circle

Problem1- Equation of Tangent to Circle

Problem 2a-Equation of Tangent to Circle

Problem D2b-Equation of Tangent to Circle

Equation of Normal to Circle

Problem-Points Lie Inside, Outside or on the Circle

Points Lie Inside, Outside or on the Circle

More on Points Lie Inside, Outside or on the Circle

Line Intersects Circle at Most 2 Points

Condition that Line may be Tangent to Circle

6.3: Analytical Proofs of Important Properties of a Circle (Practice Test)

Proof-2 Tangents can be Drawn to Circle from Point

More on Proof-2 Tangents can be Drawn to Circle from Point

Length of Tangent to Circle

To Prove Circles Diameter is 2 Times its Radius

Chords Perpendicular Passes Centre of Circle

More on Chords Perpendicular Passes Centre of Circle

Line From Centre and Midpoint of Chord is Perp to it

More on Line From Centre and Midpoint of Chord is Perp to it

Congruent Chords are Equidistance from Centre of Circle

More on Congruent Chords are Equidistant from Centre of Circle

Angle in Semicircle is Right Angle

More on Angle in Semicircle is Right Angle

Perpendicular Radial Segment is Tangent to Circle

More on Perpendicular Radial Segment is Tangent to Circle

Tangent to Circle is Perpendicular to Radial Segment

6.4: Parabola (Practice Test)

Introduction to Parabola

More on Introduction to Parabola

Terms Related to Parabola

General Form of Equation of Parabola

Other Standard Parabola

Graph of Parabola Facing Upward

Graph of Parabola Facing Downward

Graph of Parabola Facing Rightward

Graph of Parabola Facing Leftward

Problem Related with Parabola

Parabola with Vertex not at Origin

More on Parabola with Vertex not at Origin

Problem-Parabola with Vertex not at Origin

Graphing Parabola with Vertex not at Origin

More on Graphing Parabola with Vertex not at Origin

Finding Equation of Parabola with Focus and Vertex

Finding Equation of Parabola with Directrix and Vertex

Problem1-Finding Equation of Parabola with Focus and Vertex

Problem2-Finding Equation of Parabola with Focus and Vertex

Problem3-Finding Equation of Parabola with Focus and Vertex

6.5: Ellipse and Its Elements (Practice Test)

Obtaining Standard Equation of Ellipse

More on Obtaining Standard Equation of Ellipse-1

More on Obtaining Standard Equation of Ellipse-2

More on Obtaining Standard Equation of Ellipse-3

Circle as Special Case of Ellipse

Basic Terms Associated with Ellipse

More on Basic Terms Associated with Ellipse

Standard Form of Vertical and Horizontal Ellipses

Problem1-Standard Form of Vertical and Horizontal Ellipses

Translation of Horizontal Ellipse

Translation of Vertical Ellipse

More on Translation of Vertical Ellipse

Equation of Ellipse with Foci and Vertices

Problem1-Equation of Ellipse with Foci and Vertices

Problem3-Equation of Ellipse with Foci and Vertices

Ellipse Equation with Centre and Length of Axes

Ellipse Equation with Centre and Given Point

More on Ellipse Equation with Centre and Given Point

Ellipse Equation with Vertices and Eccentricity

Ellipse Equation with Vertices & Length of Semi-minor Axis

6.6: Hyperbola and Its Elements (Practice Test)

Defining Hyperbola

Standard Form of Equation of Hyperbola

More on Standard Form of Equation of Hyperbola

More on Standard Form of Equation of Hyperbola

Asymptotes of Hyperbola

Foci of Hyperbola

More on Foci of Hyperbola

Problem1-Foci of Hyperbola

Horizontal Hyperbola

Vertical Hyperbola

Rectangular Hyperbola

Graphing Hyperbola

More on Graphing Hyperbola

Problem1-Graphing Hyperbola

Problem2-Graphing Hyperbola

Hyperbola with Focus and Eccentricity

Graphing Hyperbola with Eccentricity and Latus Rectum

Graphing Hyperbola with Focus and Directrix

Translation of Hyperbola with Horizontally

More on Translation of Hyperbola with Horizontally

Translation of Hyperbola Vertically

More on Translation of Vertical Hyperbola

6.7: Tangents and Normals (Practice Test)

Intersection of Line and Parabola

More on Intersection of Line and Parabola

Equation of Tangent Line to Parabola in Slope Form

Equation of Tangent Line to Parabola at Given Point

More on Equation of Tangent Line to Parabola at Given Point

Problem-Equation of Tangent Line to Parabola at Given Point

Equation of Normal Line to Parabola at Given Point

Problem1-Equation of Normal Line to Parabola at Given Point

Application of Parabola-Suspension Related Problem

Reflecting Property of Parabola

Use of Parabola on Everyday Life-Problem

Points of Intersection of Line and Ellipse

More on Points of Intersection of Line and Ellipse

Condition of Tangency of Line to Ellipse

Equation of Tangent to Ellipse at Point

More on Equation of Tangent to Ellipse at Point

Equation of Normal to Ellipse at Point

More on Equation of Normal to Ellipse at Point

Graph of Ellipse

More on Graph of Ellipse

Point of Intersection of Line with Hyperbola

Condition of Tangency of Line to Hyperbola

Problem- Condition of Tangency of Line to Hyperbola

Equation of Tangent Line to Hyperbola at Point

More on Equation of Tangent Line to Hyperbola at Point

Problem- Equation of Tangent Line to Hyperbola at Point

Equation of Normal Line to Hyperbola at Point

More on Equation of Normal Line to Hyperbola at Point

Intersection of Two Conics

More on Intersection of Two Conics

Translation and Rotation of Axes

Translation of Axes

Problem1-Translation of Axes

Problem2-Translation of Axes

Rotation of Axes

Problem1- Rotation of axis

More on Rotation of Axes

Rotation of Conic

More on Rotation of Conic

The General Equation of Second Degree

General Degree of 2nd Degree Equation-Circle

General Degree of 2nd Degree Equation-Ellipse

General Degree of 2nd Degree Equation-Hyperbola

General Degree of 2nd Degree Equation-Parabola

Classification of Conic by Discriminant

Finding Angle of Rotation in Conic

More on Finding Angle of Rotation in Conic

Further stuff on Finding Angle of Rotation in Conic

Problem1-Finding Angle of Rotation in Conic

Chapter 7: Vectors

Introduction

Scalar and Vector Quantities

Problem-Scalar and Vector Quantities

Terminologies and Notations of Vectors

Equal Vectors

Vectors which are Opposite

Problem-Vectors which are Opposite

Column Vectors

Addition of Vectors

Problem-Addition of Vectors

Vector Addition is Associative

Problem-Vector Addition is Associative

Zero Vectors

Subtraction of Vectors

Problem-Subtraction of Vectors

Scalar Multiple of a Vector

Problem-Scalar Multiple of a Vector

Expression of a Given Vector in Terms of two Vectors

Problem-Expression of a Given Vector in Terms of two Vectors

Position Vectors

Problem-Position Vectors

Properties of Magnitude of Vector

Problem-Properties of Magnitude of Vector

More on Notation for Representing Vectors in Plane

Problem-Notation for Representing Vectors in Plane

Components of a Vector

Properties of Vectors in Plane

More on Properties of Vectors in Plane

A Unit Vector in the Direction of Another Vector

Problem-A Unit Vector in the Direction of Another Vector

Notation for Vectors in Coordinate System

Problem-Notation for Vectors in Coordinate System

The Ratio Formula in Vector

Problem1-The Ratio Formula in Vector

Problem2-The Ratio Formula in Vector

Mid-Point Theorem By Vectors

Diagonals of Parallelogram Bisect Each Other by Vectors

Ratio Theorem By Vectors

Problem-Ratio Theorem By Vectors

Introduction of Vector in Space (Practice Test)

Introducing Vector Geometry

Problem-Introducing Vector Geometry

Concept of Vector in Space

Problem-Concept of Vector in Space

More on Vectors in Space

Properties of Vectors

Problem-Properties of Vectors

Vectors Addition in Space

Problem-Vectors Addition in Space

Scalar Multiplication in Space

Problem-Scalar Multiplication in Space

Notation of Vectors in Space

Problem-Notation of Vectors in Space

Distance Between Two Points in Space

Problem-Distance Between Two Points in Space

Direction Angles and Direction Cosines of Vector

Problem-Direction Angles and Direction Cosines of Vector

The Scalar Product of Two Vectors

Scalar Product of Two Vectors

Problem-Scalar Product of Two Vectors

Properties of Scalar Product

More on Properties of Scalar Product

Problem-Properties of Scalar Product

Perpendicular Vectors

Problem-Perpendicular Vectors

Parallel Vectors

Problem-Parallel Vectors

Scalar Product of Vectors in Their Component Form

Problem-Scalar Product of Vectors in Their Component Form

Angle Between Two Vectors

Problem-Angle Between Two Vectors

Projection of One Vector Upon Another Vector

Problem-Projection of One Vector Upon Another Vector

Application of Scalar Product

Problem-Application of Scalar Product

Application of Scalar Product on Geometry

Problem-Application of Scalar Product on Geometry

More on Application of Scalar Product on Geometry

Cross Product or Vector Product of Two Vectors (Practice Test)

Cross Product of Two Vectors

Problem-Cross Product of Two Vectors

Derivation of Useful Results of Cross Product

Problem-Derivation of Useful Results of Cross Product

Expression of Cross Product in Terms of Components

Problem-Expression of Cross Product in Terms of Components

Cross Product of Unit Vectors

Properties of Cross Product

Problem-Properties of Cross Product

More on Properties of Cross Product

Analytical Expression of Cross Product

Direction Numbers or Direction Ratios

Problem-Direction Numbers or Direction Ratios

Collinear and Coplanar Vectors

Problem-Collinear and Coplanar Vectors

Vectors Application to Geometry

Problem1-Vectors Application to Geometry

Problem2-Vectors Application to Geometry

Moment of Force

Problem-Moment of Force

Condition of Parallel Vectors in Cross Product

Problem-Condition of Parallel Vectors in Cross Product

Area of Parallelogram by Vectors

Area of Triangle by Vectors

Vector Equation of Line in 3D

Problem-Vector Equation of Line in 3D

Application of Vector Equation

Problem1-Application of Vector Equation

Problem2-Application of Vector Equation

Scalar Triple Product of Vectors (Practice Test)

Scalar Triple Product

Problem-Scalar Triple Product

Vector Triple Product

More on Vector Triple Product

Analytical Expression of Triple Product

Problem-Analytical Expression of Triple Product

Volume of Parallelepiped by Triple Product

Problem-Volume of Parallelepiped by Triple Product

Volume of Tetrahedron by Triple Product

Problem-Volume of Tetrahedron by Triple Product

Properties of Triple Scalar Product

Problem-Properties of Scalar Triple Product

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**12th class math notes**

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