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Unformatted text preview: ECE 329 Homework 1 Due: June 17, 2011, 5PM 1. Consider the 3D vectors A = 3 x + y- 2 z, B = x + y- z, C = x- 2 y + 3 z, 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 = (3 , 1 ,- 2) , which is equivalent to 3 x + y- 2 z . Determine: a) The vector D A + B , b) The vector A + B- 4 C , c) The vector magnitude | A + B- 4 C | . d) The unit vector u along vector A + 2 B- C . e) The dot product A B . f) The cross product B C . 2. Let J = z 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 = z 2 ( x + y + z ) A/m 2 implies the flow of electrical current in direction J | J | = x + y +...
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