Find the vector equation of the plane passing through the point `A(1, 0, 1), B(1,-1,1) and C (4,-3,2)`

Explanation

To find the vector equation of the plane passing through the points \( A(1, 0, 1) \), \( B(1, -1, 1) \), and \( C(4, -3, 2) \), 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 AB**:
\[
\vec{AB} = B - A = (1 - 1, -1 - 0, 1 - 1) = (0, -1, 0)
...