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Vector Algebra
ElectromagneticsELE 311 Fall 2015Amer S. ZakariaDepartment of Electrical EngineeringCollege of Engineering
American University of Sharjah
Based on Sadiku 6th edition book supplementary material and class notesTitle of presentation | date 00.00.00Learning ObjectivesUnderstand the difference between scalar and vector quantities.Calculate unit vectors and vector magnitudes.Perform algebraic operations on vectors.Perform dot and cross products on vectors.
Electromagnetics | Vector AlgebraTitle of presentation | date 00.00.00Vector Algebra Scalars and Vectors
Both scalar and vector quantities can be either constant values or multivariable functions.
Electromagnetics | Vector AlgebraScalarA quantity that has only a magnitude.Examples: Mass, speed, population.Represented by simply a letter e.g. A.Title of presentation | date 00.00.00
Electromagnetics | Vector Algebra
Vector componentsUnit vectors
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Electromagnetics | Vector Algebra
Title of presentation | date 00.00.00ExampleFind magnitude and unit vector of .
Electromagnetics | Vector Algebra
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Electromagnetics | Vector Algebra
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Electromagnetics | Vector Algebra
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Electromagnetics | Vector Algebra
Title of presentation | date 00.00.00Scalar MultiplicationIf a vector is multiplied with a positive scalar: magnitude changes but not the direction.
If a vector is multiplied with a negative scalar: both magnitude and direction changes.
Electromagnetics | Vector Algebra
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Position and Distance VectorsA point P in Cartesian coordinate may be represented as (x, y, z).The position vector of point P is defined as the directed distance from the origin O(0,0,0) to P(x, y, z).
A distance vector is the displacement from one point to another.
Electromagnetics | Vector Algebra
Title of presentation | date 00.00.00Vector MultiplicationVector MultiplicationWhen two vectors are multiplied, the result is either a scalar or a vector quantity depending on multiplication type.In this course, we are interested in two types of vector multiplications:Dot (or scalar) product: Cross (or vector) product:
Electromagnetics | Vector Multiplication
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Electromagnetics | Vector Multiplication
Title of presentation | date 00.00.00Dot Product LawsThe following laws apply for dot product multiplication:Commutative Law: Distributive Law: Self Multiplication:
To find the scalar component of a vector in a certain direction:Find its scalar projection in that directionTo find the vector component in a certain direction:Find its vector projection in that direction.
Electromagnetics | Vector Multiplication
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Electromagnetics | Vector Multiplication
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Electromagnetics | Vector Multiplication
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Electromagnetics | Vector Multiplication
Title of presentation | date 00.00.00Cross Product LawsNot Commutative: Anti-Commutative: Not Associative: Distributive: Scalar Triple Product
Vector Triple Product (BAC-CAB rule)
Self Cross-Product:
Electromagnetics | Vector Multiplication
Title of presentation | date 00.00.00Cross Product using Cyclic PermutationUsing cross-products, we can show:
Electromagnetics | Vector Multiplication
Moving clockwise leads to positive results.Moving counterclockwise leads to negative results.Title of presentation | date 00.00.00End of Vector Algebra
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