\subsection{Euclidian n-Spaces}

\begin{defn}[Vector Definitions]\ \\
  \begin{itemize}
    \item $n$-vector : $v = (v_1, v_2, ..., v_n)$
    \item $\vec{PQ} // \vec{P'Q'} \implies \vec{PQ} = \vec{P'Q'}$
    \item $|| \vec{PQ} || = \sqrt{(a_2 - a_1)^2 + (b_2 - b_1)^2}$
    \item $u + v = (u_1 + v_1, u_2 + v_2), u = (u_1, u_2), v = (v_1, v_2)$
    \item $n$-vector can be viewed as a row matrix / column matrix
  \end{itemize}
\end{defn}