Find the unit vector in the direction of ` vec a+ vec b ,\ if\ vec a=2 hat i- hat j+2 hat k\ a n d\ vec b=- hat i+ hat j- hat kdot`

Explanation

To find the unit vector in the direction of \( \vec{a} + \vec{b} \), where \( \vec{a} = 2\hat{i} - \hat{j} + 2\hat{k} \) and \( \vec{b} = -\hat{i} + \hat{j} - \hat{k} \), we will follow these steps:

### Step 1: Calculate \( \vec{a} + \vec{b} \)

We start by adding the vectors \( \vec{a} \) and \( \vec{b} \):

\[
\vec{a} + \vec{b} = (2\hat{i} - \hat{j} + 2\hat{k}) + (-\hat{i} + \hat{j} - \hat{k})
...