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The flow lines (or streamlines ) of a vector field are the paths followed by a p

ID: 3079793 • Letter: T

Question

The flow lines (or streamlines ) of a vector field are the paths followed by a particle whose velocity field is the given vector field. Thus, the vectors in a vector field are tangent to the flow lines. Consider the vector field F(x,y,z) = (-7y,-7x,-7z) r(t) = ( e^(-7t)+e^(7t), e^(-7t)-e^(7t) , e^(-7t)) r'(t) = F(r(t)) = (-7 (e^(-7t)-e^(7t) ), -7 (e^(-7t)+e^(7t)) , - 7e^(-7t)) Now consider the curve r(t)= ( cos(-7t), sin(-7t), e^(-7t)) It is not a flowline of the vector field F, but of a vector field G which differs in definition from F only slightly. G (x,y,z) =

Explanation / Answer

You should get... r'(t) = F(r(t)) = .
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