Suppose $W=\{(x\_1,x\_2,x\_3)\in\mathbb{R}^3:x\_1-x\_2-x\_3=0\}$. Find a basis for $W^\perp$. 

I started by finding a basis for $W$. So since all elements of $W$ are expressible as $(x\_2+x\_3,x\_2,x\_3)=x\_2(1,1,0)+x\_3(1,0,1)$, then a basis for $W$ is $\{(1,1,0),(1,0,1)\}$. 

I am not sure, however, how to find the basis for $W^\perp$. I know that all elements in $W^\perp$ must have an inner product with $(x\_2+x\_3,x\_2,x\_3)$ equal to zero.