Find a unit vector parallel to the resultant of vectors ` vec A = 3 hat I + 3 hat j - 2 hat k` and ` vec B= hat i- 5 hat j + hat k`.

Explanation

To find a unit vector parallel to the resultant of the vectors \( \vec{A} = 3 \hat{i} + 3 \hat{j} - 2 \hat{k} \) and \( \vec{B} = \hat{i} - 5 \hat{j} + \hat{k} \), we will follow these steps:

### Step 1: Find the Resultant Vector
The resultant vector \( \vec{R} \) is obtained by adding the vectors \( \vec{A} \) and \( \vec{B} \).

\[ \vec{R} = \vec{A} + \vec{B} \]
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