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 points \( A(1, 1, -1) \), \( B(6, 4, -5) \), and \( C(-4, -2, 3) \), we can follow these steps:

### Step 1: Represent the Points in Vector Form
We can represent the points \( A \), \( B \), and \( C \) in vector form:
- \( \vec{A} = \langle 1, 1, -1 \rangle \)
- \( \vec{B} = \langle 6, 4, -5 \rangle \)
- \( \vec{C} = \langle -4, -2, 3 \rangle \)

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