Consider the force field F(x, y, z) = 8ryzi+12xyzj+4xy k, and the Helix C: r(t) =...

 

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Consider the force field F(x, y, z) = 8ry³zi+12x²y²zj+4x²y³ k, and the Helix C: r(t) = 2 costi + 2 sintj + tk from A(2,0,0) to B(0,2,5). (a) Show that F is a conservative vector field. (b) Find the work done by the force field F along the Helix C. Consider the force field F(x, y, z) = 8ry³zi+12x²y²zj+4x²y³ k, and the Helix C: r(t) = 2 costi + 2 sintj + tk from A(2,0,0) to B(0,2,5). (a) Show that F is a conservative vector field. (b) Find the work done by the force field F along the Helix C.