If the vectors `2hati+2hatj-hatk " and " 3hati-6hatj+nhatk` are mutually perpendicular, find the value of n?

Explanation

To solve the problem of finding the value of \( n \) such that the vectors \( \mathbf{A} = 2\hat{i} + 2\hat{j} - \hat{k} \) and \( \mathbf{B} = 3\hat{i} - 6\hat{j} + n\hat{k} \) are mutually perpendicular, we will use the property that the dot product of two perpendicular vectors is zero.

### Step-by-Step Solution:

1. **Identify the Vectors:**
- Let \( \mathbf{A} = 2\hat{i} + 2\hat{j} - \hat{k} \)
- Let \( \mathbf{B} = 3\hat{i} - 6\hat{j} + n\hat{k} \)

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