Find the point of intersection of line passing through `(0,0,1)` and the intersection lines `x+2u+z=1,-x+y-2za n dx+y=2,x+z=2` with the `x y` plane.

Explanation

To find the point of intersection of the line passing through (0, 0, 1) and the intersection of the given planes with the xy-plane, we will follow these steps:

### Step 1: Identify the equations of the planes
The equations of the planes given in the problem are:
1. \( P_1: x + 2y + z - 1 = 0 \)
2. \( P_2: -x + y - z = 0 \)
3. \( P_3: x + y - 2 = 0 \)
4. \( P_4: x + z - 2 = 0 \)
...