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1.Find the divergence of the vector point function = -2x+2y at the point (1,-1,1).?
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1.Find the divergence of the vector point function = -2x+2y at the poi...

Calculation of Divergence of the Vector Field

The divergence of a vector field F = -2x+2y is given by the formula div(F) = ∇ ⋅ F, where ∇ is the del operator.

Step 1: Calculate the partial derivatives
- The partial derivatives of the vector field F = -2x+2y are:
- ∂/∂x = -2
- ∂/∂y = 2
- ∂/∂z = 0

Step 2: Evaluate the divergence at the given point
- At the point (1, -1, 1), the divergence of the vector field F is:
- div(F) = ∂/∂x(-2x) + ∂/∂y(2y) + ∂/∂z(0)
- div(F) = -2 + 2 + 0
- div(F) = 0

Therefore, the divergence of the vector field F = -2x+2y at the point (1, -1, 1) is 0.
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1.Find the divergence of the vector point function = -2x+2y at the point (1,-1,1).?
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