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yarga
11 days ago
15

Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then

the following is true. ∂P ∂y = ∂Q ∂x ∂P ∂z = ∂R ∂x ∂Q ∂z = ∂R ∂y . Since F is conservative, there exists a function f such that F = ∇f, that is, P, Q, and R are defined as follows. (Enter your answers in the form fx, fy, fz.)
Mathematics
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