Find the equation of the plane through the line of intersection of the planes `x + y + z = 1` and `2x + 3y + 4z = 5`which is perpendicular to the plane `x - y + z = 0`.

Explanation

To find the equation of the plane through the line of intersection of the planes \( x + y + z = 1 \) and \( 2x + 3y + 4z = 5 \) which is perpendicular to the plane \( x - y + z = 0 \), we can follow these steps:

### Step 1: Identify the equations of the given planes
The equations of the two planes are:
1. \( P_1: x + y + z - 1 = 0 \)
2. \( P_2: 2x + 3y + 4z - 5 = 0 \)

### Step 2: Write the general equation of the plane through the line of intersection
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