Find a unit vector perpendicular to each of the vectors `hati+2hatj-3hatk` and `hati-2hatj+hatk`.

Explanation

To find a unit vector that is perpendicular to both vectors \( \mathbf{A} = \hat{i} + 2\hat{j} - 3\hat{k} \) and \( \mathbf{B} = \hat{i} - 2\hat{j} + \hat{k} \), we will use the cross product of the two vectors. Here are the steps:

### Step 1: Write down the vectors
We have:
\[ \mathbf{A} = \hat{i} + 2\hat{j} - 3\hat{k} \]
\[
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