How can I find work done for a particle to go from $(2,2,1)$ to $(1,-1,2)$ in a force field $
$$F(x,y,z)=\left(y+y^2z,\, x-z+2xyz,\, -y+xy^2\right)$$
Work done for a particle in a force field
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vector-fields
1 Answers
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Line integral, of course:
$$C: r(t):=t(1,-1,2)+(2,2,1)=(t+2,\,-t+2,\,2t+1)\;,\;\;0\le t\le 1\implies$$
$$W=\int_C\vec F\bullet d\vec r=\int_0^1 F(r(t))\bullet r'(t)dt=\ldots$$