329fall08hw1

329fall08hw1 - ECE 329 1. Let Homework 1 Due: Sept 2, 2008,...

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ECE 329 Homework 1 Due: Sept 2, 2008, 5PM 1. Let A = 3ˆ x y - z, B x y - ˆ z, C 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 Fux 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.)
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329fall08hw1 - ECE 329 1. Let Homework 1 Due: Sept 2, 2008,...

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