Limit of a sequence that arises from product

Question

Let $(x_n)$ and $(y_n)$ be two sequences in $\mathbb{R}^d$ such that

1. $(x_n)$ converges to $\bar{x}$ and
2. for every $n$ we have $\langle x_n,y_n\rangle=0$.

Is it true that $\lim_{n\to \infty}\langle\bar{x},y_n\rangle=0$?