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Unformatted text preview: f with f = F , but rst we should check the equations F 1 /y = F 2 /x F 1 /z = F 3 /x and F 2 /z = F 3 /y . Since they fail, the vector eld is not conservative. 4. We can parameterize the line segment by R = t Q + (1 t ) P = (1 t, 1 + t, t ) for 0 t 1. Then d R /dt = ( 1 , 1 , 1) and F ( R ) = (1 t, 1 t 2 , 0). Thus the answer is i 1 (1 t, 1 t 2 , 0) ( 1 , 1 , 1) dt = i 1 (( t 1) + (1 t 2 )) dt = 1 2 / 2 1 3 / 3 = 1 / 6 . 5. Since the eld is conservative and we are integrating around a closed curve, the integral is zero....
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This note was uploaded on 06/18/2009 for the course MATH 20E taught by Professor Enright during the Spring '07 term at UCSD.
 Spring '07
 Enright
 Vector Calculus, Vectors, Dot Product

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