Orthogonal Complement

Question

"Let $\Bbb{V}$ be a vector space with an inner product $<\cdot,\cdot>$, and $S\subset\Bbb{V}$. We define the orthogonal complement of $S$, denoted by $S^{\perp}$, as follows:
$$S^{\perp}=\left\{v\in\Bbb{V}|<v,u>=0,\forall u\in S\right\}.$$ Let $\Bbb{V}=\Bbb{R}^2$ with the usual sum and product by scalar, and $S=\{(x,y)\in\Bbb{R}^2|x+y=1\}.$ Find $S^{\perp}$."
I have done this exercise but I don't know if it is correct. I found $S^{\perp}=\{(0,0)\}$. Is that right?