If ` vec a= hat i+ hat j- hat k ,\ vec b=- hat i+2 hat j+2 hat k\ a n d\ vec c=- hat i+2 hat j- hat k ,` then a unit vector normal to the vectors `a+b\ a n d\ b-c` is ` hat i` b. ` hat j` c. ` hat k` d. none of these

Explanation

To find a unit vector normal to the vectors \( \vec{a} + \vec{b} \) and \( \vec{b} - \vec{c} \), we will follow these steps:

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