---

Closed form

… is

\[\begin{equation*}
  \| \vec{u} - \vec{v} \|
  = \left\|
  \begin{pmatrix} u_1 \\ \vdots \\ u_m \end{pmatrix}
  -
  \begin{pmatrix} v_1 \\ \vdots \\ v_m \end{pmatrix}
  \right\|
  = \sqrt{{(u_1 - v_1)}^2 + \cdots + {(u_m - v_m)}^2}.
\end{equation*}
\]