Find a unit vector perpendicular to both the vectors `(2hat(i)+3hat(j)+hat(k))` and `(hat(i)-hat(j)-2hat(k))`.

Explanation

To find a unit vector 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 follow these steps:

### Step 1: Calculate the Cross Product
To find a vector that is perpendicular to both \( \mathbf{A} \) and \( \mathbf{B} \), we need to compute the cross product \( \mathbf{A} \times \mathbf{B} \).

The formula for the cross product in determinant form is:
\[
\mathbf{A} \times \mathbf{B} = \begin{vmatrix}
...