# hw1 - ECE 329 Homework 1 Due 5PM 1 Let A = 3 y 2 B = x y z...

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ECE 329 Homework 1 Due: Aug 31, 2010, 5PM 1. Let A = 3ˆ x + ˆ y - z, B = ˆ x + ˆ y - ˆ z, C = ˆ x - y + 3ˆ z, where ˆ x , ˆ y , and ˆ 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 ˆ 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.) 2. Charges Q 1

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## This note was uploaded on 11/06/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw1 - ECE 329 Homework 1 Due 5PM 1 Let A = 3 y 2 B = x y z...

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