Find a set of vectors reciprocal to the set `-hati+hatj+hatk,hati+hatk,hati+hatj+hatk`

Explanation

To find a set of vectors reciprocal to the set \(\mathbf{A} = -\hat{i} + \hat{j} + \hat{k}\), \(\mathbf{B} = \hat{i} + \hat{k}\), and \(\mathbf{C} = \hat{i} + \hat{j} + \hat{k}\), we will follow these steps:

### Step 1: Define the vectors
Let:
\[ \mathbf{A} = -\hat{i} + \hat{j} + \hat{k} \]
\[
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