Find a unit vector perpendicular to each of the vector ` vec a+ vec b` and ` vec a- vec b` , where ` vec a=3 hat i+2 hat j+2 hat k` and ` vec b= hat i+2 hat j-\ 2 hat k`

Explanation

To find a unit vector that is perpendicular to both vectors \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \), we can follow these steps:

### Step 1: Define the vectors
Given:
\[ \vec{a} = 3 \hat{i} + 2 \hat{j} + 2 \hat{k} \]
\[
...