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Let k1dx+k2dy+k3dz be a constant 1-form and let a, b, c be any 3 point in...

Let k1dx+k2dy+k3dz be a constant 1-form and let a, b, c be any 3 point in the x,y,z space. Prove that the integral of this 1-form from a to c is the sum of the integral from a to b plus the integral from b to c

Using the results, prove that the amount of work done by a constant force field in moving a particle from a to b along a path composed of a straight line segments is independent of the path.

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