Final answer:
The question is unclearly formulated as it does not provide a direct link between the given scalar field and an electric field. If we assume the scalar field represents the electric potential, the electric field would be the negative gradient of the scalar field. However, without additional information or explicit context, we cannot determine electric field components or direction angle.
Step-by-step explanation:
The question is asking for the calculation of the gradient of the scalar field Φ(x, y, z) = x³ y³ e^(4yz) at a specific point and then to use this information to answer questions related to the electric field. However, the questions about the electric field itself, such as its components or rate of change, are not properly formulated. Typically, one would need to define an electric field in relation to the potential Φ to answer these parts. As such, without a clear link between the scalar field and an electric field, we cannot directly calculate electric field components or the direction angle E of the electric field vector.
If Φ were the electric potential, we could find the electric field by calculating the negative gradient of Φ. In general, the electric field E is related to the electric potential Φ by the vector equation E = -∇Φ, where ∇ is the gradient operator. The direction of the electric field at a point is in the direction of the greatest decrease of potential, and its magnitude at that point is the rate of change of the potential with respect to displacement in that direction.
It's important to understand that the rate of change of a scalar field is a general concept that can apply to various physical scenarios. In the context of electrostatics, the scalar field would represent the electric potential, and the rate of change would indicate the electric field strength. However, in the given problem, more context is needed to relate the scalar field with an electric field directly.