Find the distance between the point `P(6, 5, 9)`and the plane determined by the points `A (3, 1, 2)`, `B (5, 2, 4)`and `C( 1, 1, 6)`.

Explanation

To find the distance between the point \( P(6, 5, 9) \) and the plane determined by the points \( A(3, 1, 2) \), \( B(5, 2, 4) \), and \( C(1, 1, 6) \), we will follow these steps:

### Step 1: Find the vectors AB and AC
We first need to find the vectors \( \overrightarrow{AB} \) and \( \overrightarrow{AC} \).

\[ \overrightarrow{AB} = B - A = (5 - 3, 2 - 1, 4 - 2) = (2, 1, 2) \]
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