Answer
$$\langle 2,0,1 \rangle.$$
(Other solutions are possible.)
Work Step by Step
Assume that the vector is $\langle a, b,c \rangle $, since the vectors are orthogonal, then we have
$$\langle a,b,c \rangle \cdot \langle-1,2,2\rangle=0\Longrightarrow -a+2b+2c=0.$$
We can pick any vector $\langle a,b,c \rangle$ that satisfies the above equation. Hence, we can choose the vector as follows
$$ a=2, b=0, c=1$$ That is the vector is given by $$\langle 2,0,1 \rangle.$$
(Many other vectors are possible.)
