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

Explanation

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

### Step 1: Define the vectors
Let:
- \( \mathbf{a} = -\hat{i} + \hat{j} + \hat{k} \)
- \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \)
- \( \mathbf{c} = \hat{i} + \hat{j} + \hat{k} \)

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