Unformatted text preview: x ( t ) = (sin t,et , cos t ) is a ﬂow line of the vector ﬁeld F = ( z,y,x ). 4. Find the curl of the vector ﬁeld F = z i + ( x + y 2 ) j + x 2 yz k . Verify that div (curl F ) = 0. 5. ( § 3.4 no.23) Establish the identity ∇ · ( f F ) = f ∇ · F + F · ∇ f , where f : R n → R is a function, and F is a vector ﬁeld in R n . ( Hint : Write F = ( F 1 ,F 2 ,...,F n ) if F is a vector ﬁeld in R n .) 1...
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 Spring '11
 wang
 Multivariable Calculus, Vector Calculus, UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS, MATH1211 Multivariable Calculus

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