Final answer:
In the context of geometric continuity equations with fixed points A and D having zero velocities, the correct statement among the options provided is c. VA = VD, as it directly reflects the given conditions.
Step-by-step explanation:
The question at hand involves geometric continuity equations relevant to vector fields, often applied in physics and engineering. Given that points A and D are fixed with velocities VA = VD = 0, we can deduce the following:
- Equation ∇^2V = 0 represents Laplace's equation, which suggests that the scalar potential V is harmonic within a region if it satisfies this equation. This would be correct if the region is free from any sources or sinks of the field.
- The equation ∇VA = ∇VD implies that the gradient of potential at points A and D are the same, which doesn't necessarily relate to the condition of zero velocities at these points.
- VA = VD is a valid statement since it's given that the velocities at both points are zero, adhering to the conditions provided.
- ∇^2VD = 0 is similar to the first equation, indicating that the scalar potential at point D also satisfies Laplace's equation, which could be true assuming D is in a region free from sources or sinks of the field and VD is a scalar potential.
Among these options, c. VA = VD is undoubtedly correct since it exactly states the given condition that both velocities are zero.