The plane `x-y-z=2` is rotated through `90^(@)` about its line of intersection with the plane `x+2y+z=2`. The distance of `(-1,-2,-1)` from the plane in the new position is `lamda sqrt(6/7)`. Then the value of `lamda` is equal to

Explanation

To solve the problem step by step, we need to find the value of \( \lambda \) given the conditions of the planes and the point.

### Step 1: Identify the planes
We have two planes:
1. Plane 1: \( P_1: x - y - z - 2 = 0 \)
2. Plane 2: \( P_2: x + 2y + z - 2 = 0 \)

### Step 2: Find the line of intersection of the two planes
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