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# 329fall11hw1 - ECE 329 Homework 1 Due 5PM 1 Review...

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ECE 329 Homework 1 Due: August 26, 2011, 5PM 1. Review exercises on vectors: Consider the 3D vectors A = 2ˆ x + ˆ z (1) B = 1 2 ˆ x + 1 4 ˆ y + 2ˆ z (2) C = 4ˆ y - z (3) where ˆ x (1 , 0 , 0) , ˆ y (0 , 1 , 0) , and ˆ z (0 , 0 , 1) constitute an orthogonal set of unit vectors directed along the principal axes of a right-handed Cartesian coordinate system. Vectors can also be represented in component form: e.g., A = (2 , 0 , 1) , B = ( 1 2 , 1 4 , 2) , and C = (0 , 4 , - 4) . Determine the following: a) The vector B - C b) The vector A - 2 B + 4 C c) The vector magnitude | A - 2 B + 4 C | d) The unit vector ˆ u along 3 A - 2 C e) The scalar dot product B · C f) The vector cross product A × B g) The scalar triple product A · ( B × C ) 2. Let J = y 2 x + ˆ y + ˆ z ) A/m 2 denote the electrical current density field — i.e., current flux per unit area — in a region of space represented in Cartesian coordinates. A current density of J = y 2 x + ˆ y + ˆ z ) A/m 2 implies the flow of electrical current in direction J | J | = ˆ x y z 3 with a magnitude of | J | = y 2 3 amperes (A) per unit area.

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329fall11hw1 - ECE 329 Homework 1 Due 5PM 1 Review...

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