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Unformatted text preview: using two different coordinate systems: a) Cylindrical coordinates b) Spherical coordinates. 2
4. (18pts) Sketch the vector field F ( x, y ) y , x , 0 in the x‐y plane, and calculate its curl. Find the set of points where the curl equals zero, and use your sketch to explain why the curl should be expected to be zero at these points. 2
5. (24 pts) Consider vector field F ( x, y ) 2 xy z cos( xz ), x , x cos( xz ) 1 . a) Show that F is conservative b) Find the potential function of this vector field. c) Use curve parameterization to directly calculate its line integral along the path in the figure, where C1 is a parabola from the origin to point (1,0,1) and C2 is a straight line from (1,0,1) to (1,1,1). d) Compare the result in part (c) to the line integral value obtained using the potential function...
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