Electromagnetic Theory and Applications

# Electromagnetic Theory and Applications - Vector Analysis...

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9/1/2007 1 Vector Analysis Vectors vs. Scalars A vector is a quantity having both magnitude and direction. A scalar is a quantity only having magnitude. A unit vector has magnitude one and is used to denote direction. To find the unit vector of vector A: The magnitude of vector A: 2 2 2 z y x A A A + + = A 2 2 2 z y x A z z y y x x A A A u A A A + + = = + + = A A A u u u A

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9/1/2007 2 unit vectors z y x u u u A 12 4 3 + + = 13 12 4 2 2 2 + + A A A u A = 3 = = 13 12 4 3 z y x A u u u u + + = MATLAB A =[A A A ] A x y A z ]; norm (A) A = [3 4 12]; a = norm (A); a 13
9/1/2007 3 Vector Algebra • Vectors can be added and subtracted. • They obey associative,cummutative, and distributive laws A+(B+C)=(A+B)+C A+B=B+A r(A+B)=rA+rB V t M lti li ti h t f Vector Multiplication has two forms: • Dot Product (scalar) • Cross Product (vector) a =1 u +2 u +3 u >>a=[123] vectors addition x y z b = 3 u x + 2 u y + 1 u z c = a + b c = 4 u x + 4 u y + 4 u z >> a = [1 2 3]; >> b = [3 2 1]; >> c = a + b; c = 4 4 4

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Electromagnetic Theory and Applications - Vector Analysis...

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