Find the vector and cartesian equations of the plane which passes through the point `(5, 2, 4)`and perpendicular to the line with direction ratios `(2, 3, 1)`.

Explanation

To find the vector and Cartesian equations of the plane that passes through the point \( (5, 2, 4) \) and is perpendicular to the line with direction ratios \( (2, 3, 1) \), we can follow these steps:

### Step 1: Identify the normal vector
The direction ratios of the line give us the normal vector of the plane. Here, the direction ratios are \( (2, 3, 1) \), so the normal vector \( \mathbf{n} \) can be expressed as:
\[ \mathbf{n} = 2\mathbf{i} + 3\mathbf{j} + 1\mathbf{k} \]

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