15_2_1 - φ( x , y , z ) = x 2 2-y 2 + 3 z 2 2 is a...

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1. F = x i - 2 y j + 3 z k , F 1 = x , F 2 = - 2 y , F 3 = 3 z . We have F 1 y = 0 = F 2 x , F 1 z = 0 = F 3 x , F 2 z = 0 = F 3 y . Therefore, F may be conservative. If F = φ , then ∂φ x = x , ∂φ y = - 2 y , ∂φ z = 3 z . Evidently
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Unformatted text preview: φ( x , y , z ) = x 2 2-y 2 + 3 z 2 2 is a potential for F . Thus F is conservative on 3 ....
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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