Answer
$$\langle -2,1,0 \rangle.$$
Work Step by Step
Assume that the vector $\langle a, b,c \rangle $ is orthogonal to $\langle 1,2,1 \rangle $, then we have
$$\langle a,b,c \rangle \cdot \langle 1,2,1\rangle=0\Longrightarrow a+2b+c=0 .$$
We can pick any vector $\langle a,b,c \rangle$ that satisfies the above equation. Hence we can choose a vector as follows
$$\langle -2,1,0 \rangle.$$
One can see that $\langle -2,1,0 \rangle $ is orthogonal to $\langle 1,2,1 \rangle $ and not orthogonal to $\langle 1,0,-1 \rangle $ because their dot product would not be 0.
