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Unformatted text preview: (3 ,3 , 2) Â· ( x1 ,y1 ,z1) = 0 , that is,3 x3 y + 2 z =4 . 1 Question 4. By utilizing independence of path, one could compute this integral directly by using any curve from (1,2,3) to (2,2,2); an example of one such path would be Ï† ( t ) = (1 + t, 2 , 3t ) , â‰¤ t â‰¤ 1 . However, it is worth nothing that the function f ( x,y,z ) = xyz is a potential function for F ; i.e., âˆ‡ f = F . Thus, by the Fundamental Theorem of Line Integrals, Z Ï† F d s = f (2 , 2 , 2)f (1 , 2 , 3) = 2 . Question 5. a ) Since the divergence of a vector ï¬eld is an expression denoting the level of compression within that ï¬eld, and div ( curl ( F )) = 0 for any smooth vector ï¬eld F , this statement is TRUE . b ) The curl of a vector ï¬eld is a measure of rotational force that a vector ï¬eld applies; since the curl of a gradient ï¬eld is 0, this statement is TRUE . 2...
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 Fall '07
 Enright
 Vector Calculus, Vector field

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