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Multivariable & Vectorhard
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A particle moves along a conical helix parameterized by r⃗(t)=⟨tcos⁡t,tsin⁡t,t⟩\vec{r}(t) = \langle t \cos t, t \sin t, t \rangler(t)=⟨tcost,tsint,t⟩ for t∈[0,2π]t \in [0, 2\pi]t∈[0,2π]. Calculate the work done on the particle by the force field F⃗(x,y,z)=⟨−y,x,z2⟩\vec{F}(x, y, z) = \langle -y, x, z^2 \rangleF(x,y,z)=⟨−y,x,z2⟩.