The length of the projection of the line segment joining the points `(5,-1,4)` and `(4,-1,3)` on the plane `x+y+z=7` is

Explanation

To find the length of the projection of the line segment joining the points \( A(5, -1, 4) \) and \( B(4, -1, 3) \) on the plane \( x + y + z = 7 \), we can follow these steps:

### Step 1: Find the direction vector of the line segment \( AB \)
The direction vector \( \vec{AB} \) can be calculated as:
\[ \vec{AB} = B - A = (4 - 5, -1 - (-1), 3 - 4) = (-1, 0, -1) \]

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