Distance of Vectors

Definition

Let

• $\mathbf{u}=(u_1,u_2,\dots ,u_n)$ points in $R^n$
• $\mathbf{v}=(v_1,v_2,\dots ,v_n)$ points in $R^n$

Then the distance between $\mathbf{u}$ and $\mathbf{v}$ denoted by $d(\mathbf{u},\mathbf{v})$ is defined by

$$d(\mathbf{u},\mathbf{v})=||\mathbf{u}-\mathbf{v}||=\sqrt{(u_1-v_1{)}^2+(u_2-v_2{)}^2+\cdots +(u_n-v_n{)}^2}$$