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Unformatted text preview: ECE 329 Homework 1 Due: August 26, 2011, 5PM 1. Review exercises on vectors: Consider the 3D vectors A = 2 x + z (1) B = 1 2 x + 1 4 y + 2 z (2) C = 4 y- 4 z (3) where x (1 , , 0) , y (0 , 1 , 0) , and z (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 , , 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 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 + y + 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 + y + z ) A/m 2 implies the flow of electrical current in direction...
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This note was uploaded on 01/26/2012 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08