329fall08hw1sol

329fall08hw1sol - ECE-329 Fall 2008 Homework 1 (Solution)...

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Unformatted text preview: ECE-329 Fall 2008 Homework 1 (Solution) September 3, 2008 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 magnitude of ~ A + ~ B- 4 ~ C = 10 y- 15 z is ~ A + ~ B- 4 ~ C = p 10 2 + 15 2 = 325 . (b) The unit vector of ~ A + 2 ~ B- ~ C = 4 x + 5 y- 7 z is u = 4 x + 5 y- 7 z 4 2 + 5 2 + 7 2 = 4 x + 5 y- 7 z 90 . (c) The dot product ~ A ~ B = (3 x + y- 2 z ) ( x + y- z ) = 3 + 1 + 2 = 6 . (d) 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. (e) The scalar triple product ~ A ~ B ~ C = (3 x + y- 2 z ) ( x- 4 y- 3 z ) = 3- 4 + 6 = 5 . (f) 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. (g) If vector ~ C has velocity units (m / s), ~ B has flux density units (Tesla), and ~ A has distance units (m), then the units of ~ A ~ B ~ C would be m s Tesla m = Joules Coulomb , this unit describes energy per unit charge. 2. Charge Q 1 = 8 o C is placed at ~ r 1 = (- 1 , , 0) and generates ~ E 1 ( x,y,z ) = Q 1 4 o ~ r- ~ r 1 | ~ r- ~ r 1 | 3 = 2 ( x + 1) x + y y + z...
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329fall08hw1sol - ECE-329 Fall 2008 Homework 1 (Solution)...

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