## Calculus (3rd Edition)

$$\langle -2,1,0 \rangle.$$
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.