Determine a unit vector perpendicular to both the vectors `vecA=2hati-3hatj+6hatk and vecB=hati-2hatj+4hatk`

Explanation

To determine a unit vector that is perpendicular to both vectors \(\vec{A} = 2\hat{i} - 3\hat{j} + 6\hat{k}\) and \(\vec{B} = \hat{i} - 2\hat{j} + 4\hat{k}\), we will follow these steps:

### Step 1: Calculate the Cross Product of \(\vec{A}\) and \(\vec{B}\)

The cross product \(\vec{A} \times \vec{B}\) can be calculated using the determinant of a matrix formed by the unit vectors \(\hat{i}\), \(\hat{j}\), and \(\hat{k}\) and the components of the vectors \(\vec{A}\) and \(\vec{B}\).

\[
\vec{A} \times \vec{B} =
...