Find a vector of magnitude 6, which is perpendicular to both the vectors `2hati-hatj+2hatkand4hati-hatj+3hatk`.

Explanation

To find a vector of magnitude 6 that is perpendicular to both vectors \( \mathbf{a} = 2\hat{i} - \hat{j} + 2\hat{k} \) and \( \mathbf{b} = 4\hat{i} - \hat{j} + 3\hat{k} \), we can follow these steps:

### Step 1: Calculate the Cross Product of Vectors \( \mathbf{a} \) and \( \mathbf{b} \)

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}
...