Find a unit vector perpendicular to each one of the vectors `vec(a) = 4 hat(i) - hat (j) + 3hat(k)` and `vec(b) = 3 hat(i) + 2 hat(j) - hat(k)`.

Explanation

To find a unit vector that is perpendicular to both vectors \(\vec{a} = 4 \hat{i} - \hat{j} + 3 \hat{k}\) and \(\vec{b} = 3 \hat{i} + 2 \hat{j} - \hat{k}\), we can use the cross product of these two vectors. The steps are as follows:

### Step 1: Write down the vectors
We have:
\[ \vec{a} = 4 \hat{i} - \hat{j} + 3 \hat{k} \]
\[
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