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Consider F and C below. F(x, y, z) = yz i + xz j + (xy...

Consider F and C below.

F(x, y, z) = yz i + xz j + (xy + 12z) k

C is the line segment from (2, 0, −3) to (4, 6, 3)

(a) Find a function f such that F = ∇f.

f(x, y, z) =

  

  

(b) Use part (a) to evaluate

  
C

∇f · dr along the given curve C.

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