ECE 329 Spring 2009

ECE 329 Spring 2009 - ECE-329 Spring 2009 Homework 1...

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Unformatted text preview: ECE-329 Spring 2009 Homework 1 Solution January 26, 2009 1. Given vectors A = 3 x + y- 2 z, B = x + y- z, C = x- 2 y + 3 z, we can calculate the following. a) The vector D = A + B = 4 x + 2 y- 3 z. b) The vector A + B- 4 C = 10 y- 15 z. c) The vector magnitude | A + B- 4 C | = 10 2 + 15 2 = 325 . d) The unit vector u = A +2 B- C | A +2 B- C | = 4 x +5 y- 7 z 4 2 +5 2 +7 2 = 4 x +5 y- 7 z 90 . e) The dot product A B = (3 x + y- 2 z ) ( x + y- z ) = 3 + 1 + 2 = 6 . f) The cross product B C = x y z 1 1- 1 1- 2 3 = (3- 2) x- (3 + 1) y + (- 2- 1) z = x- 4 y- 3 z. g) The scalar triple product A ( B C ) = (3 x + y- 2 z ) ( x- 4 y- 3 z ) = 3- 4 + 6 = 5 . h) If vectors A , B , and C have units of meters, then the units of A ( B C ) would be m 3 . | A ( B C ) | is the volume of a parallelepiped formed by these vectors. 2. Volume integral review. Given the charge density ( x,y,z ) = x 2 + y 2 + z 2 C / m 3 , the total electric charge contained in a cube of volume V = 8 m 3 centered at the origin is (1 , 1 , 1) (- 1 , 1 , 1) (- 1 , 1 ,- 1) (1 , 1 ,...
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ECE 329 Spring 2009 - ECE-329 Spring 2009 Homework 1...

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