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Definition: If F = Pi + Qj + Rk is a vector field on R^3 and the partial derivatives of P, Q, and R all exist, then the curl of F is the vector field on R^3 defined by curl F = (dR/dy - dQ/dz)i + (dP/dz - dR/dx)j + (dQ/dx - dP/dy)k.
Source: Multivariable Calculus, 7th edition by James Stewart