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Unformatted text preview: ECE 329 Homework 1 Due: Jan 22, 2008, 5PM 1. Let A = 3 x + y- 2 z, B = x + y- z, C = x- 2 y + 3 z, where x , y , and z denote an orthogonal set of unit vectors directed along the principal axes of a right-handed Cartesian coordinate system (denoted as a x , a y , and a z in the text). Calculate: a) The vector magnitude | A + B- 4 C | . b) The unit vector u along the vector A + 2 B- C . c) The dot product A B . d) The cross product B C . e) The scalar triple product A ( B C ) . f) If vectors A , B , C above are measured in units of meters, what would be the unit of the triple product A ( B C ) and what would be the geometrical interpretation of | A ( B C ) | ? g) If vector C has velocity units (m/s), B has magnetic flux density units (T), and A has distance units (m), what would be the unit of the scalar triple product A ( B C ) ? What physical parameter would the unit describe? (Hint: you can think in terms of a Lorentz force analogy.)parameter would the unit describe?...
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This note was uploaded on 04/14/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.
- Spring '08