Title of presentation here
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
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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
