Find a unit vector perpendicular to each of the vectors `( veca+ vecb)`and `( veca- vecb)`, where ` veca= hat i+ hat j+ hat k , vecb= hat i+2 hat j+3 hat k`.

Explanation

To find a unit vector perpendicular to the vectors \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \), where \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} + 3\hat{k} \), we can follow these steps:

### Step 1: Calculate \( \vec{a} + \vec{b} \)
\[ \vec{a} + \vec{b} = (\hat{i} + \hat{j} + \hat{k}) + (\hat{i} + 2\hat{j} + 3\hat{k}) \]
\[
= (1 + 1)\hat{i} + (1 + 2)\hat{j} + (1 + 3)\hat{k}
...