Find a unit vector perpendicular to both the vectors `(2hati+3hatj+hatk) and (hati-hatj+2hatk)`.

Explanation

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

### Step 1: Calculate the Cross Product
The cross product \( \mathbf{A} \times \mathbf{B} \) can be calculated using the determinant of a matrix formed by the unit vectors \( \hat{i}, \hat{j}, \hat{k} \) and the components of vectors \( \mathbf{A} \) and \( \mathbf{B} \).

\[
\mathbf{A} \times \mathbf{B} = \begin{vmatrix}
\hat{i} & \hat{j} & \hat{k} \\
...