If the force is given by F=2x-y+z)i+ x+y-z^2)j +3x-2y+4z)k find the work done by a moving particle around a closed path C in the xy plane. If the circle has centre at the origin and radius 3 . Is this work done path independent??

The force F, given by F=2x-y+z)i+ x+y-z^2)j +3x-2y+4z)k can be used to calculate the work done by a moving particle around a closed path C in the xy plane. In this case, we are looking at a circle with centre at the origin and radius 3. The work done is calculated as follows:

First, we need to find out how much displacement there is along each coordinate axis (dx, dy and dz). Since our path C is a circle in the xy plane only dx and dy need to be considered; since it has radius of 3 these displacements will both equal 3. Therefore, dx = 3 and dy = 3.

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