Let $n\in$ \reftext{def:natural-numbers-2026a}{$\mathbb{N}$}, and let $x=(x_1,\dots,x_n)$ and $y=(y_1,\dots,y_n)$ be points of \reftext{def:euclidean-space-rn-2026a}{Euclidean space} $\mathbb{R}^n$.

1. The \textbf{difference} $x-y$ is the point of $\mathbb{R}^n$ defined by

where in each coordinate the difference is that of real numbers. 2. The \textbf{dot product} of $x$ and $y$ is the real number

3. The points $x$ and $y$ are called \textbf{orthogonal} if $x\cdot y=0$.