Dine the unit vector peroendicular to each of the vectors ` 3 hat i+ hat j 2 hat k` and ` 2 hat i- 2 hat j = 4 hat k`.

Explanation

To find the unit vector perpendicular to the given vectors \( \mathbf{A} = 3 \hat{i} + \hat{j} + 2 \hat{k} \) and \( \mathbf{B} = 2 \hat{i} - 2 \hat{j} + 4 \hat{k} \), we will follow these steps:

### Step 1: Find the Cross Product of the Vectors
The first step is to calculate the cross product \( \mathbf{A} \times \mathbf{B} \). The formula for the cross product of two vectors in component form is given by the determinant of a matrix formed by the unit vectors \( \hat{i}, \hat{j}, \hat{k} \) and the components of the vectors.

\[
\mathbf{A} \times \mathbf{B} =
\begin{vmatrix}
...