The number of vectors of unit length perpendicular to the vectors $\overrightarrow {\rm{a}} = 2\widehat {\rm{i}} + \widehat {\rm{j}} + 2\widehat {\rm{k}}$ and $\overrightarrow {\rm{b}} = \widehat {\rm{j}} + \widehat {\rm{k}}$ is

The number of vectors of unit length perpendicular to the vectors
$\overrightarrow {\rm{a}}$ and $\overrightarrow {\rm{b}}$ is $\overrightarrow {\rm{c}}$ (say)

i.e., $\overrightarrow {\rm{c}} = \pm (\overrightarrow {\rm{a}} \times \overrightarrow {\rm{b}} )$

So, there will be two vectors of unit length perpendicular to the vectors

$\overrightarrow {\rm{a}}$ and $\overrightarrow {\rm{b}}$.