Find the coordinates of the point where the line through `(3, 4, 5)`and `(2, 3, 1)`crosses the plane`2x + y + z = 7`.

Explanation

To find the coordinates of the point where the line through the points (3, 4, 5) and (2, 3, 1) crosses the plane defined by the equation \(2x + y + z = 7\), we can follow these steps:

### Step 1: Determine the Direction Vector of the Line
The direction vector \(\mathbf{b}\) of the line can be found by subtracting the coordinates of the two points:
\[ \mathbf{b} = (2 - 3, 3 - 4, 1 - 5) = (-1, -1, -4) \]

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