Find the vector equation of the plane passing through the points `(1,1,0),(1,2,1)a n d(-2,2,-1)dot`

Explanation

To find the vector equation of the plane passing through the points \( A(1, 1, 0) \), \( B(1, 2, 1) \), and \( C(-2, 2, -1) \), we can follow these steps:

### Step 1: Find two vectors in the plane
We can find two vectors that lie in the plane by subtracting the coordinates of the points:

1. Vector \( \vec{AB} = B - A = (1 - 1, 2 - 1, 1 - 0) = (0, 1, 1) \)
2. Vector \( \vec{AC} = C - A = (-2 - 1, 2 - 1, -1 - 0) = (-3, 1, -1) \)

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