3. Use Stokes' Theorem to evaluate F.dr where F =ri-4zj+ryk and C is is the circle of radius 1 at r = -3 and perpendicular to the r-axis. C has a counter ciockwise rotation if you are looking down the r-axis from the positive r-axis to the negative r-axis. See the figure below for a sketch of the curve.

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A: Answer

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Q: find the Cerrvature of the Curve x:(0,1|R? defined by x(t)=14Cost, 1sint,o), where %3D is coostant 2

A: α(t)=(1rcost ,1rsint ,0)r is constantTo find the curvature of the given curve

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Q: Find T, N, and k for the plane curve r(t) = ti+ In (cos t) j. -5<t<5. T(t) = i+Oi %3D

A: Given: r(t)=t i+lncos tj,  -π2&lt;t&lt;π2 Formulas to obtain T, N and k are given as:…

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Q: Let F(x, y, z) = (6xyz+4x) i+(3x²z+ze")j+(3x²y-e=v) k, and let C be the portion of the parametric…

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