Given the vector field F(x, y, z) = 2xze'i+xzej+x?ek do the following: (a) Determine whether F...

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Given the vector field F(x, y, z) = 2xze'i+xze"j+x?e"k do the following: (a) Determine whether F is a conservative field. If it is, find its potential. (b) Compute the circulation F.dr where C is the first octant part of the ellipse r2+4y? 4 on the plane z = 1 traversed counterclockwise around the z-axis. %3D (c) Compute the circulation $F dr where C is now the whole ellipse from part (b). Explain your answer. Given the vector field F(x, y, z) = 2xze'i+xze"j+x?e"k do the following: (a) Determine whether F is a conservative field. If it is, find its potential. (b) Compute the circulation F.dr where C is the first octant part of the ellipse r2+4y? 4 on the plane z = 1 traversed counterclockwise around the z-axis. %3D (c) Compute the circulation $F dr where C is now the whole ellipse from part (b). Explain your answer.