\[
\displaylines{\text{If }k\ge2\text{ and }\mathbf{x}\in\mathbb{R}^{k}\text{ show that there exists }\mathbf{y}\in\mathbb{R}^{k}\text{ such that }\mathbf{y}\ne\mathbf{0}\text{ but }\mathbf{x}\cdot\mathbf{y}=0\\ \text{Is this also true if }k=1?\\ }
\]