Find the vector equation of a plane passing through three points A(0, 0, 2), B(1, -1, 1), C(3, 4, 5) .

Explanation

To find the vector equation of a plane passing through the points A(0, 0, 2), B(1, -1, 1), and C(3, 4, 5), we can follow these steps:

### Step 1: Identify the position vectors of the points
Let:
- \( \vec{A} = \begin{pmatrix} 0 \\ 0 \\ 2 \end{pmatrix} \)
- \( \vec{B} = \begin{pmatrix} 1 \\ -1 \\ 1 \end{pmatrix} \)
- \( \vec{C} = \begin{pmatrix} 3 \\ 4 \\ 5 \end{pmatrix} \)

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