Find the vector equations of the plane passing through the points `R(2, 5, -3)`, `S ( -2, -3, 5)`and `T(5, 3, -3)`.

Explanation

To find the vector equation of the plane passing through the points \( R(2, 5, -3) \), \( S(-2, -3, 5) \), and \( T(5, 3, -3) \), we will follow these steps:

### Step 1: Find the position vectors of the points
Let:
- \( \vec{R} = \begin{pmatrix} 2 \\ 5 \\ -3 \end{pmatrix} \)
- \( \vec{S} = \begin{pmatrix} -2 \\ -3 \\ 5 \end{pmatrix} \)
- \( \vec{T} = \begin{pmatrix} 5 \\ 3 \\ -3 \end{pmatrix} \)

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