If ` veca`= `hat i+ hat j+ hat k`,` vecb=2 hat i- hat j+3 hat k` and ` vecc= hat i-2 hat j+ hat k`find a unit vector parallel to the vector `2 veca- vec b+3 vecc`.

Explanation

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

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