Find the equations of the planes that passes through three points.(a)(1,1,-1),(6,4,-5),(-4,-2,3)

Explanation

To find the equation of the plane that passes through the three given points \( A(1, 1, -1) \), \( B(6, 4, -5) \), and \( C(-4, -2, 3) \), we can follow these steps:

### Step 1: Define the position vectors of the points
Let:
- \( \vec{A} = \begin{pmatrix} 1 \\ 1 \\ -1 \end{pmatrix} \)
- \( \vec{B} = \begin{pmatrix} 6 \\ 4 \\ -5 \end{pmatrix} \)
- \( \vec{C} = \begin{pmatrix} -4 \\ -2 \\ 3 \end{pmatrix} \)

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