Find the unit vector of `(vec(A)+vec(B))` where `vec(A)=2hati-hatj+3hatk` and `vec(B)=3hati-2hatj-2hatk`.

Explanation

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

### Step 1: Add the vectors \( \vec{A} \) and \( \vec{B} \)

We start by adding the two vectors component-wise:

\[
\vec{A} + \vec{B} = (2\hat{i} - \hat{j} + 3\hat{k}) + (3\hat{i} - 2\hat{j} - 2\hat{k})
...