Difference, Dot Product, and Orthogonality in $\mathbb{R}^n$

Let $n\in$ $\mathbb{N}$, and let $x=(x_1,\dots,x_n)$ and $y=(y_1,\dots,y_n)$ be points of Euclidean space $\mathbb{R}^n$.

1. The 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 dot product of $x$ and $y$ is the real number

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