329sp09hw1 - ECE 329 Homework 1 Due: Jan 27, 2009, 5PM 1....

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ECE 329 Homework 1 Due: Jan 27, 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 (denoted as a x , a y , and a z in the text, respectively) 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 . g) The scalar triple product A · ( B × C ) . h) 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 ) | ? 2. Volume integral review: Let ρ ( x,y,z )= x 2 + y 2 + z 2 C/m 3 denote the electrical charge density function — i.e., charge per unit volume — in a region of space represented in Cartesian coordinates.
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329sp09hw1 - ECE 329 Homework 1 Due: Jan 27, 2009, 5PM 1....

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