Find a unit vector perpendicular to the lane containing the vectors ` vec a=2 hat i+ hat j+ hat k\ a n d\ vec b= hat i+2 hat j+ hat kdot`

Explanation

To find a unit vector perpendicular to the plane containing the vectors **a** and **b**, we can use the cross product of these vectors. Here’s a step-by-step solution:

### Step 1: Define the vectors
Given:
\[ \vec{a} = 2\hat{i} + \hat{j} + \hat{k} \]
\[
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