ECE329 - ECE 329 Homework 1 Due: June 18, 2009, 5PM 1....

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ECE 329 Homework 1 Due: June 18, 2009, 5PM 1. Review exercises on vectors: Consider the 3D vectors A = 3ˆ x y - z, B x y - ˆ C x - y + 3ˆ 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 = (3 , 1 , - 2) , which is equivalent to x y - 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 ˆ u along vector A +2 B - C . e) The dot product A · B . f) The cross product B × C . 2. A particle with charge q =1 C passing through the origin r =( x, y, z ) = 0 of the lab frame is observed to accelerate with forces F 1 = 3ˆ F 2 F 3 = 3ˆ z + 4ˆ y N when the velocity of the particle is v 1 =0 , v 2 = 1ˆ y, v 3 = 2ˆ z m s , in turns. Use the Lorentz force equation F = q ( E + v × B ) to determine the Felds E and B at the origin.
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ECE329 - ECE 329 Homework 1 Due: June 18, 2009, 5PM 1....

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