If $\vec a =\hat i+\hat j-\hat k, \vec b = −\hat i+2\hat j+2\hat k$ and $\vec c =-\hat i+2\hat j-\hat k$, then a unit vector normal to the vectors $\vec a +\vec b$ and $\vec b-\vec c$, is

$\hat i$

We have,

$\vec a +\vec b=3\hat j+\hat k$ and $\vec b-\vec c=3\hat k$

$∴(\vec a +\vec b)×(\vec b-\vec c)=(3\hat j+\hat k)×3\hat k=9\hat i$

So, required unit vector = $\hat i$