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

Explanation

To find 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 can follow these steps:

### Step 1: Understand the condition for perpendicular vectors
Two vectors are mutually perpendicular if their dot product is zero. Therefore, we need to compute the dot product of vectors \( \mathbf{A} \) and \( \mathbf{B} \) and set it equal to zero.

### Step 2: Write down the vectors
We have:
\[
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