Find a vector perpendicular to vector `vec(A)=(hat(i)+2hat(j)-3hat(k))` as well as `vec(B)=(hat(i)+hat(j)-hat(k))`

Explanation

To find a vector that is perpendicular to both vectors \(\vec{A} = \hat{i} + 2\hat{j} - 3\hat{k}\) and \(\vec{B} = \hat{i} + \hat{j} - \hat{k}\), we can use the cross product of the two vectors. The cross product of two vectors yields a vector that is perpendicular to both.

### Step-by-Step Solution:

1. **Identify the vectors**:
\[ \vec{A} = \hat{i} + 2\hat{j} - 3\hat{k} \]
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