notes 1 - EE468G NOTES (1) Reading assignment: Chapter 1...

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EE468G NOTES (1) Reading assignment: Chapter 1 Contents: Unit Vectors, Vectors, Vector operations Vectors in three coordinate systems Vector : A quantity that has magnitude and direction Examples : Force, velocity, field intensity Notation and writting : or A or A A Unit vector : a vector whose magnitude is 1. Examples: x a x ˆ is a unit vector pointing in x-direction, ˆ y is a unit vector pointing in y-direction. Vector representation in rectangular coordinate system: component format z y x y x x a a a C a a B a A 2 2 7 3 , x y x y x y z 2 2 1 -7 3 5 In general, a vector has three components x A , y A , z A : z z y y x x a A a A a A A , Component x A is the projection of vector A on x-axis. Calculation of magnitude : 222 x y z A A A A . Examples: y x a a B 7 3 58 0 ) 7 ( 3 | | 2 2 2 B Direction of a vector : The direction of a vector can be described by three angles that the vector made with the x-axis, y-axis, and z-axis, respectively. In the above examples,
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y x a a B 7 3 It makes an angle of   1 cos 3 58 66.8 o with x-axis, It makes an angle of   1 cos 7 58 156.8 o  with y-axis, It makes an angle of   1 cos 0 58 90 o with z-axis. In general, if z z y y x x a A a A a A A , the angles it makes with x-, y-, and z-components are: z , , and xy   , where       1 1 1 cos , cos , cos x x y y z z A A A A A A Vector operations : Addition and subtraction z z y y x x a A a A a A A z z y y x x a B a B a B B , Addition of A and B : z z z y y y x x x a B A a B A a B A B A ) ( ) ( ) ( Subtraction of A and B : z z z y y y x x x a B A a B A a B A B A ) ( ) ( ) ( The results of addition and subtraction are vectors.
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This note was uploaded on 01/19/2012 for the course EE 461 taught by Professor Cambron during the Spring '11 term at Ohio State.

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notes 1 - EE468G NOTES (1) Reading assignment: Chapter 1...

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