Equation of lines and planes - 1 of 8

JIM 319 VECTOR CALCULUS

Introduction: Equation of lines and planes - 1

Distance between 2 lines

Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Equation of Lines and planes- 2 of 8

JIM 319 VECTOR CALCULUS

Equation of line in space ( Vector Equation )




Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Equation of lines and Planes - 3 of 8

JIM 319 VECTOR CALCULUS

Examples:-

1. To determine the points given, lies on the given plane
2. To find the vector equation, parametrics and symmetry equations for the line L,that passes through the given points
3. To find the point that the line L in ( 2 ) above,intersects the xy-plane

Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Equation of Lines and Planes - 4 of 8

JIM 319 VECTOR CALCULUS
5 More Examples




Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Equtions of Lines and Planes - 5 of 8

JIM 319 VECTOR CALCULUS

1. Equations of Planes
2. Equation of a plane is space ( Parametric Equations )

Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Equation of Lines and Planes - 6 of 8

JIM 310 VECTOR CALCULUS
Comparing Equations of Lines and Planes



Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Equations of Lines and Planes - 7 of 8

JIM 310 VECTOR CALCULUS
Comparing Equations of Lines and Planes
More Examples

1. To find the scalar equation of a plane through one given point and parallel to another given plane
2. To find the scalar equation of a plane that contain line ,L and is parallel to another given plane
3. To find the scalar equation of a plane that passes through 3 given points
4. To find the scalar equation of a plane that passes through a given point and contains line,L

Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Equations of Lines and Planes - 8 of 8 Angles

JIM 310 VECTOR CALCULUS

1. Angles between Intersecting Planes
2. Lines of Intersection Between Planes
3. Sketching Planes In Space

Next Topics in Equations of Lines and Planes

1. Introduction
2. Vector Equations ,Parametric Equations and Symmetric Equations
3. Examples on ( 2 ) 
4. Five more Challenging Examples on( 2 ) 
5. Equations of Planes
6. Comparing Equations of Lines and Planes
7. Examples of scalar Equations
8. Angles of Intersecting Planes

Surah Al Baqarah -Sheikh Mishari Rasyid

Qari : Sheikh Mishari Rasyid



Pautan Selanjutnya :-

Cross Product - 2 Componen Definition

JIM 319 VECTOR CALCULUS







Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product - 4 Example

JIM 319 VECTOR CALCULUS



Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product -5 Proof OF Algebraic Properties

JIM 319 VECTOR CALCULUS



Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product - 6 Geometric Properties

JIM 319 VECTOR CALCULUS



Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product -8 Application Torque

JIM 319 VECTOR CALCULUS
Torque



Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product -9 Example on Torque

JIM 319 VECTOR CALCULUS
 Example On Torque



Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product - 7 Scalar Triple Product

JIM 319 VECTOR CALCULUS

Scalar Triple Product- Volume of Parallelepiped
                                   - Coplanar 
Note : Parallelepiped - A polyhedron whose faces are all parallelograms



Proof
 
Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product - 3 Examples

JIM 319 VECTOR CALCULUS



Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Cross Product-1 Geometric Definition

JIM 219 VECTOR CALCULUS

1. Cross Product -Geometric Definition
2. Comparison between Dot Product and Cross Product

Cross Product - Related Topics

1. Geometric Definition
2. Component Definition
3. Examples
4. More Examples
5. Proof-Algebraic Properties
6. Geometric Properties
7. Scalar Triple Product-Volume of a parallelepiped
8. Application-Torque
9. Example on Torque

THE DOT PRODUCT

Dot Product-12 Parallelogram Law

JIM 319 VECTOR CALCULUS

1. Cauchy-Schawrt Inequality
2. Triangle Inequality
3. Parallelogram Law

Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product - 11 Application

JIM 319 VECTOR CALCULUS
Application In Physics



Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product- 10 Direction Angles Direction Cosines

JIM 319 VECTOR  CALCULUS



Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product -8 Scalar Vector Orthogonal Projection

JIM 319 Vector Calculus
Scalar,Vector and Orthogonal Projection



Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product - 7 unit vector

Unit Vectors which form angles between the vectors

Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product -6 Angle of Triangles

JIM 319 VECTOR CALCULUS

1. Unit Vectors
2. Angles of Triangles
3. Orthogonal
4. Parallel

Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product- 5 Angle Between Vector

JIM 319 VECTOR CALCULUS
Dot Product - Proof Angles Between Vectors 7 Examples




Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product -4 More Examples

JIM 319 VECTOR CALCULUS
More examples -Angles,Perpendicular

Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Dot Product-3 Examples

JIM 319 VECTOR CALCULUS

Examples

Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

The Dot Product - 2 Properties

Properties  of dot product

 Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

The Dot Product -1

JIM 319 VECTOR CALCULUS

1. Geometric Definition
2. Angle between 2 vectors : Consider 5 Cases

Dot Product -Related Topics

1. Geometric Definition
2. Properties
3. Examples
4. More examples
5. Examples on angles between 2 vectors
6. Orthogonal,Parallel Vectors
7. Unit Vector
8. Scalar Vector,Orthogonal & Parallel
9. NIL
10. Direction Angles &  Direction Cosines
11. Application of Dot Product
12. Proof: Parallelogram Law

THE CROSS PRODUCT

Free English Coversion Workshop

Free English Conversation Workshop

Speak better English in 30 minutes a week

Spoken English is demanded in the job market. You can start preparing now with Come Chat with Me (CCWM), a free English conversation workshop held at USM’s Pusat Pengajian Bahasa, Literasi dan Terjemahan (PPBLT).

˜ CCWM is open to any USM enrolled student and runs from 10 September to 19 December 2019.

˜ Taught by a native-English speaker, CCWM offers a mentoring environment where students receive individualized attention—with no grades, exams or points to worry about.

˜ Students attend one (1) 30-minute session weekly. Enrollment is free and accepted on an ongoing basis, subject to space available. You do not need to be currently enrolled in any USM English course to attend CCWM.

Chat session times are:

Monday–Thursday

0930, 1015, 1100, 1145

1400, 1445

To register, please email Language Instructor Lance Ong at ongla@usm.my with your:

1. Full name

2. MUET or IELTS Band number

3. Your final year and final semester before graduating

4. Matric number, international office (IO) number, Intensive English Program (IEP) number, or other form of proof that you're currently enrolled at USM

5. IC number

6. Important: Please request 3 time slots in order of your first, second, and third preference. Your Chat time will be one of these times for the entire semester. Example: if you specify 1) Tue 0930, 2) Wed 1015, 3) Thu 1400 and are assigned to Wed 1015, you will be expected to attend Chat on Wednesdays at 1015 each week for the entire semester. To the extent possible, we will endeavour to accommodate your first preference, but as enrolment increases into the semester, we cannot unconditionally guarantee first preferences.

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Pusat Pengajian Bahasa, Literasi dan Terjemahan

Universiti Sains Malaysia