[7] a) Show that the vector F=(x+2y+4z)i + (2x-3y-z)j +(4x-y-22) is irrotational and find its scalar...

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[7] a) Show that the vector F=(x+2y+4z)i + (2x-3y-z)j +(4x-y-22) is irrotational and find its scalar potential. [7] b) Find the directional derivative of xyz + xz at (1, 1, 1) in a direction of the normal to the surface 3xy² + y = z at (0, 1, 1). c) Find the angle between the normal to the surface x² = yz at the points (1, 1, 1) and (2, 4, 1). [6] [7] a) Show that the vector F=(x+2y+4z)i + (2x-3y-z)j +(4x-y-22) is irrotational and find its scalar potential. [7] b) Find the directional derivative of xyz + xz at (1, 1, 1) in a direction of the normal to the surface 3xy² + y = z at (0, 1, 1). c) Find the angle between the normal to the surface x² = yz at the points (1, 1, 1) and (2, 4, 1). [6]

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