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12th Class Math Sindh Board

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Chapter 1: Function and Limits 37 videos

1.1: Introduction  Numbers Systems

Definition & Notation of Some Important Sets

1.2: Intervals    

Defining Interval

Defining Closed, Open, Half Open and Half Closed Interval

1.3: Modulus Function    

The Modulus of a Function

1.4: Neighborhood

Introduction to Neighborhood in Intervals

1.5: Binary Relation    

Introduction to Binary Relation

Problem-Introduction to Binary Relation

Problem 1: Introduction to Binary Relation

Domain & Range of Binary Relation

Problem-Domain & Range of Binary Relation

Problem 1: Domain & Range of Binary Relation

1.6: Functions    

Introduction to Function

Problem 1: Introduction to Function

More on Introduction to Functions

1.7: Inverse Function

Inverse of a Function

1.8: Concept of Function in Terms of Variables    

Introduction to Function

1.9: Algebra of Functions

Algebraic Functions

1.10: Polynomial Function

Algebraic Functions

1.11: Rational Function

Constant, Identity and Rational Functions

1.12: Composite Function

Composition of a Functions

1.13: Even and Odd Function

Even and Odd Functions

1.14: Circular Trigonometric Function

Trigonometric Functions

1.15: Inverse Trigonometric Function

Introduction to Binary Operations

1.16: Formulization of Functions

Formulization of Functions

1.17: Graph of a Relation and of a Function

Graphical Representation of Functions

1.18: Sequence

Defining Sequence and Limit of Sequence

1.19: Limit of Sequence

Defining Sequence and Limit of Sequence

1.20: Bounded Set and Monotonic Sequence

Bounded Set and Monotonic Sequence

1.21: Divergence

Convergent and Divergent Sequence

1.22: Exponential Function    

Operations on Residue Classes Modulo n

1.23: Logarithmic Function

Properties of Binary Operations

1.24: Infinite Series

The Infinite Geometric Series

1.25: Meaning of the Phrase ‘x’ Tends to ‘a’

Meaning of Phrase x Approaches to a

1.26: Limit of Function

Concept of a Limit of a Function

1.27: Limits as x Tends Infinity    

Limit at Infinity

Method for Evaluating the Limits at Infinity

Deducting Formulae at Limit Approaches to 0 and infinity

Chapter 2: The Straight Line 50 videos

2.1: Cartesian Coordinate System

Cartesian Coordinate System & Cartesian Plane

2.2: Distance Between Two Given Points  

Derivation of Distance formula

Use of Distance formula

Problem 1: Use of Distance formula

2.3: Division of Given Line Segment in a Given Ratio  

Points Dividing the Join of Two Points in Given Ratio

More on Points Dividing Join of Two Points in Given Ratio

Problem1a-Points Dividing the Join of Two Points in Given Ratio

Problem1b-Points Dividing the Join of Two Points in Given Ratio

2.4: Rules For the Choice of Axes

Rules For the Choice of Axes

2.5: Curves and Equations

Curves and Equations

2.6: Slope or Gradient of a Line  

Inclination of Line

Slope or Gradient of a Line

Gradient of a Straight Line Joining Two Points

2.7: Slope of the Line Joining Two Given Points

Gradient of a Straight Line Joining Two Points

2.8: Condition For Three Points to be Collinear

Slope of Collinear Line Segments

2.9: Parallel and Perpendicular Lines  

Slope of Parallel Lines

Problem-Slope of Parallel Lines

Problem2-Slope of Parallel Lines

Relationship between Two and Three Straight Lines

2.10: Angle From One Line to Another in the Slope Form

Angle Between Two Lines

Problem1-Angle Between Two Lines

Problem2-Angle Between Two Lines

2.11: Lines Parallel to the Axes of Coordinates  

Slope or Gradient of a Line

2.12: Various Forms of Equation of Straight Line  

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

2.13: Deduction of One Form of an Equation of a Line From Another  

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

Chapter 3: The General Equation of Straight Lines 35 videos

3.1: The General Linear Equation

How 2 Variabled Linear Equation Represent Straight Line

Problem1-How 2 Variabled Linear Equation Represent Straight Line

3.2: Angle Between Two Lines From l2 to l1 in The General Form

Angle Between Two Lines in General Form

3.3: Points of Intersection of Two Straight Lines

The Point of Intersection of Straight Lines

Problem1-The Point of Intersection of Straight Lines

3.4: Concurrency of Three 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

3.5: Equations of Lines in the Matrix Form

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

3.6: Lines Through the Intersection of Two Given Lines

Equation of Lines Through Point of Intersecting 2 Lines

Problem1-Equation of Lines Through Point of Intersecting 2 Lines

3.7: Position of a Point with Respect to a Given Straight Line  

Position of Point with Respect to Line

More on Position of Point with Respect to Line

Problem1-Position of Point with Respect to Line

3.8: Distance of a Point From a Line  

Distance of Point From Line

Problem1-Distance of Point From Line

Distance between Two Parallel Lines

Problem1-Distance between Two Parallel Lines

3.9: Area of a Triangle  

Area of Triangular Region With Given Vertices

More on Area of Triangular Region With Given Vertices

Problem1-Area of Triangular Region With Given Vertices

3.10: Equation of a Pair of Straight Lines Through the Origin

Equation of a Pair of Straight Lines Through the Origin

3.11: The General Quadratic Equation   

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’

Problem2-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 4: Differentiability 49 videos

4.1: Derivative of a Function at a Point  

Derivative of a Function

More on Derivative of a Function

Notation for Derivative

Derivative by First Principle

More on Derivative by First Principle

Problem1-Derivative by First Principle

Problem2-Derivative by First Principle

Derivative of a Constant Function

Power Rule for Differentiation

More on Power Rule for Differentiation

Problem-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

Problem1a-Derivative of Quotient

Derivative of Trigonometric Functions

More on Derivative of Trigonometric Functions

More Stuff on Derivative of Trigonometric Functions

Problem1-Derivative of Trigonometric Functions

Problem2-Derivative of Trigonometric Functions

Problem3-Derivative of Trigonometric Functions

4.2: Composite Function  

Differentiation by Chain Rule

More on Differentiation by Chain Rule

Problem1-Differentiation by Chain Rule

Problem2-Differentiation by Chain Rule

Derivative of Inverse Trigonometric Functions

More on Derivative of Inverse Trigonometric Functions

Problem1-Derivative of Inverse Trigonometric Functions

Problem2-Derivative of Inverse Trigonometric Functions

Problem3-Derivative of Inverse Trigonometric Functions

Derivative of Exponential Functions

Problem1-Derivative of Exponential Functions

Derivative of Logarithmic Functions

Problem1-Derivative of Logarithmic Functions

Problem Solving-Logarithmic Functions

4.3: Implicit Function

Implicit Differentiations

Problem-Implicit Differentiations

Problem-Implicit Differentiations

4.4: Parametric Function

Derivative of Parametric Equations

Problem1-Derivative of Parametric Equations

4.5: Higher Derivatives  

Introducing Higher Order Differentiation

Problem1-Introducing Higher Order Differentiation

Problem2-Introducing Higher Order Differentiation

Problem3-Introducing Higher Order Differentiation

Problem4-Introducing Higher Order Differentiation

Chapter 6: Antiderivatives 93 videos

6.1: Antiderivation or Integration  

Antidifferentiation and Indefinite Integral

Integral Language and Notation

Difference between Delta y and dy

Problem1-Difference between Delta y and dy

Theorems on Anti-derivative

Problem1-Theorems on Anti-derivative

Problem2-Theorems on Anti-derivative

Problem3-Theorems on Anti-derivative

Problem4-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 Fucntions

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

6.2: Integration by Substitution  

Integration by Substitution

Some Useful Substitutions in Integration

More on Some Useful Substitions in Integration

Some More Useful Substitions in Integration

Problem-Integration by Useful Substitution

Problem2-Some More Useful Substitions in Integration

Prolem3-Some More Useful Substitions in Integration

Prolem4-Some More Useful Substitions in Integration

Prolem5-Some More Useful Substitions in Integration

6.3: Integration by Completing the Squares

Integration by Completing Square

Integration by Completing Square

6.4: Integration by Parts  

Integration by Parts

More on Integration by Parts

Problem1-Integration by Parts

Problem2-Integration by Parts

Problem2b-Integration by Parts

Integration by Parts of Trigonometric Functions

More on Integration by Parts of Trigonometric Functions

6.5: Partial Fractions  

Integrating Partial Fractions with Non-repeated Factors

Problem1-Integrating Partial Fractions with Non-repeated Factors

Problem1a-Integrating Partial Fractions with Non-repeated Factors

More on Integrating Partial Fractions with Non-repeated Factors

Integrating Partial Fractions with Non-repeated Linear Factors

Problem1-Integrating Partial Fractions with Non-repeated Linear Facto

Problem1a-Integrating Partial Fractions with Non-repeated Linear Fact

More on Integrating Partial Fractions with Non-repeated Factors

Integrating Partial Fractions with Non-Repeated Quadratic Factors

Problem1-Integrating Partial Fractions with Non-Repeated Quadratic Fa

Problem1a-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

6.6: Integation of Rational Fractions

Integration of Rational Fractions

6.7: Area Under a Curve  

The Definite Integral

Problem1-The Definite Integral

Problem2-The Definite Integral

Problem2a-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 Integation

Area Bounded by Two Curves Above and Below x-axis

Application of Definite Integral

More on Application of Definite Integral

Problem1-Application of Definite Integral

Problem2-Application of Definite Integral

Problem2a-Application of Definite Integral

Problem3-Application of Definite Integral

Problem3a-Application of Definite Integral

6.8: Differential Equations  

Introduction to Differential Equation

More on Introduction to Differential Equation

Classification of Differential Equation

More on Classification of Differnetial Equation

Solving First Order Differential Equation

More on Solving First Order Differential Equation

Problem1-Solving First Order Differential Equation

Problem2-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 7: Circle 38 videos

7.1: Introduction  

Introduction to Conic Section

More on Introduction to Conic Section

7.2: Equation of a Circle  

Standard Form of Equation of Circle

General Form of Equation of Circle

More on General Form of Equation of Circle

7.3: Equation of a Circle with a Line Segment as its Diameter

Equation of Circle Passing Through 2 Points and its Centre on Line

7.4: Tangents and Normals to a Circle  

Equation of Tangent to Circle

More on Equation of Tangent to Circle

Problem1- Equation of Tangent to Circle

Problem2a-Equation of Tangent to Circle

Problem2b-Equation of Tangent to Circle

Equation of Normal to Circle

7.5: Equation of the Chord Joining Two Points on the Circle

Chords Perpendicular Passes Centre of Circle

More on Chords Perpendicular Passes Centre of Circle

7.6: Points of Intersection of the Straight Line and the Circle

Line Intersects Circle at Most 2 Points

7.7: Condition of Tangency of a Line to a Circle

Condition that Line may be Tangent to Circle

7.8: The Equation of Tangents and Normals Using Derivatives  

Equation of Tangent to Circle

More on Equation of Tangent to Circle

Problem1- Equation of Tangent to Circle

Problem2a-Equation of Tangent to Circle

Problem2b-Equation of Tangent to Circle

Equation of Normal to Circle

7.9: Length of the Tangent from the Point to the Circle

Length of Tangent to Circle

7.10: Condition of Normality

Equation of Normal to Circle

7.11: Some Geometrical Properties of the Circle  

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 Equidistance from Centre of Circle

Angle in Semi-Circle is Right Angle

More on Angle in Semi-Circle is Right Angle

Perpendicular Radial Segment is Tangent to Circle

More on Perpendicular Radial Segment is Tangent to Circle

Chapter 8: Parabola,Ellipse and Hyperbola 109 videos

8.1: General Conic  

Introduction to Conic Section

More on Introduction to Conic Section

8.2: Parabola  

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

8.3: The Standard Equation of an Ellipse  

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

More on 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

8.4: Hyperbola  

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

8.5: Equation of Chords

Equation of Chords to Parabola

8.6: Equations of Tangents and Normals to Conics  

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

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

Problem1a-Equation of Normal to Ellipse at Point

Problem1b-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

8.7: TwoTangents and Condition of Tangency to Conics  

Equation of Tangent Line to Parabola in Slope Form

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

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

Problem1a-Equation of Normal to Ellipse at Point

Problem1b-Equation of Normal to Ellipse at Point

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

Chapter 9: Vectors 100 videos

9.1: Cartesian Coordinate System for 3D Space  

Introducing Vector Geometry

Problem-Introducing Vector Geometry

Concept of Vector in Space

More on Vectors in Space

Problem-Concept of Vector in Space

9.2: Scalar and Vectors Quantities  

Scalar and Vector Quantities

Problem-Scalar and Vector Quantities

Terminologies and Notations of Vectors

9.3: Equal Vectors

Equal Vectors

9.4: Position Vector and its Direction Cosines  

Position Vectors

Problem-Position Vectors

Direction Angles and Direction Cosines of Vector

Problem-Direction Angles and Direction Cosines of Vector

9.5: Multiplication of a Vector by a Scalar

Scalar Multiple of a Vector

Problem-Scalar Multiple of a Vector

9.6: Vector Addition  

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

9.7: Components of a Vector in a 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

9.8: Application to Analytic Geometry  

Problem-Moment of Force

Vectors Application to Geometry

Problem1-Vectors Application to Geometry

Problem2-Vectors Application to Geometry

Moment of Force

9.9: The Scalar and Vector Products 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

More on Application of Scalar Product on Geometry

Problem-Application of Scalar Product on Geometry

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

9.10: Scalar Products of Three Vectors  

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

9.11: Applications of Vectors to Mechanics  

Area of Parallelogram by Vectors

Area of Triangle by Vectors

Application of Vector Equation

Problem1-Application of Vector Equation

Problem2-Application of Vector Equation

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