If ` vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d\ vec c= hat i-2 hat j+ hat k` find a unit vector parallel to `2 vec a- vec b+3 vec cdot`

Explanation

To find a unit vector parallel to \(2 \vec{a} - \vec{b} + 3 \vec{c}\), we will follow these steps:

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