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 three points A(0, 0, 2), B(1, -1, 1), and C(3, 4, 5), we will follow these steps:

### Step 1: Identify the position vectors of the points
The position vectors of the points A, B, and C can be represented as:
- \( \vec{A} = 0 \hat{i} + 0 \hat{j} + 2 \hat{k} = 2 \hat{k} \)
- \( \vec{B} = 1 \hat{i} - 1 \hat{j} + 1 \hat{k} = \hat{i} - \hat{j} + \hat{k} \)
- \( \vec{C} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k} \)

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