Find a unit vector perpendicular to both the vectors `4 hat i- hat j+3 hat k\ a n d-2 hat i+ hat j-2 hat kdot`

Explanation

To find a unit vector that is perpendicular to both vectors \( \mathbf{A} = 4 \hat{i} - \hat{j} + 3 \hat{k} \) and \( \mathbf{B} = -2 \hat{i} + \hat{j} - 2 \hat{k} \), we will use the cross product. Here’s the step-by-step solution:

### Step 1: Write down the vectors
Let:
\[ \mathbf{A} = 4 \hat{i} - \hat{j} + 3 \hat{k} \]
\[
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