## Calculus (3rd Edition)

$$\langle 2,0,1 \rangle.$$ (Other solutions are possible.)
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.)