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Unformatted text preview: (-3 ,-3 , 2) ( x-1 ,y-1 ,z-1) = 0 , that is,-3 x-3 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 ( t ) = (1 + t, 2 , 3-t ) , t 1 . However, it is worth nothing that the function f ( x,y,z ) = xyz is a potential function for F ; i.e., f = F . Thus, by the Fundamental Theorem of Line Integrals, Z F d s = f (2 , 2 , 2)-f (1 , 2 , 3) = 2 . Question 5. a ) Since the divergence of a vector eld is an expression denoting the level of compression within that eld, and div ( curl ( F )) = 0 for any smooth vector eld F , this statement is TRUE . b ) The curl of a vector eld is a measure of rotational force that a vector eld applies; since the curl of a gradient eld is 0, this statement is TRUE . 2...
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This note was uploaded on 04/30/2008 for the course MATH 20E taught by Professor Enright during the Fall '07 term at UCSD.
- Fall '07
- Vector Calculus