Find the Cartesian equation of the plane passing through point A(1, 2, 3) and which is
perpendicular to a vector `vecn=2hati-3hatj+4hatk`

Explanation

To find the Cartesian equation of the plane that passes through the point A(1, 2, 3) and is perpendicular to the vector \(\vec{n} = 2\hat{i} - 3\hat{j} + 4\hat{k}\), we can use the formula for the equation of a plane in three-dimensional space.

### Step-by-Step Solution:

1. **Identify the Normal Vector and Point**:
The normal vector \(\vec{n}\) is given as \(2\hat{i} - 3\hat{j} + 4\hat{k}\), which can be represented as \((a, b, c) = (2, -3, 4)\). The point through which the plane passes is \(A(1, 2, 3)\), which gives us the coordinates \((x_1, y_1, z_1) = (1, 2, 3)\).

2. **Use the Plane Equation Formula**:
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