Find the vector and the Cartesian equation of the plane which pases through the point (5,2,-4) and perpendicular to the line with direction ratios (2,3,-1).

Explanation

To find the vector and Cartesian equation 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 Point and Direction Ratios
The point through which the plane passes is given as \( P(5, 2, -4) \). The direction ratios of the line, which are also the direction ratios of the normal vector to the plane, are given as \( (2, 3, -1) \).

### Step 2: Write the Position Vector of the Point
The position vector \( \mathbf{A} \) of the point \( P(5, 2, -4) \) can be expressed as:
\[
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