What is the magnitude of the electric field at the point `( -1.00 overset(^)(i) - 2.00 overset(^) (j) + 4.00 overset(^)(k) )m` if the electric potential in the region is given by `V= 2.00 xyz^(2)`, where `V` is in volts and coordinates x, y, and z are in meters?

Explanation

To find the magnitude of the electric field at the point \((-1.00 \hat{i} - 2.00 \hat{j} + 4.00 \hat{k}) \, m\) given the electric potential \(V = 2.00 xyz^2\), we will follow these steps:

### Step 1: Calculate the Electric Field Components
The electric field \(\mathbf{E}\) can be derived from the electric potential \(V\) using the relation:

\[ \mathbf{E} = -\nabla V = -\left( \frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k} \right) \]
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