If the vectors given by `vec(A) = hat(i) + 2hat(j) + 2hat(k) and vec(B) = hat(i) - hat(j) + n hat(k)` are prerpendicular to each other find the value of n .

Explanation

To find the value of \( n \) such that the vectors \( \vec{A} \) and \( \vec{B} \) are perpendicular, we can use the property that the dot product of two perpendicular vectors is zero.

### Step-by-Step Solution:

1. **Identify the Vectors**:
- Given:
\[
\vec{A} = \hat{i} + 2\hat{j} + 2\hat{k}
...