Vector addition

The sum of vectors u and v is

$\mathbf{u}+\mathbf{v} =(u_1+v_1)\mathbf{e}_1 +(u_2+v_2)\mathbf{e}_2 +(u_3+v_3)\mathbf{e}_3.$

Where

${\mathbf u} = {\mathbf u_1}{\mathbf e_1} + {\mathbf u_2}{\mathbf e_2} + {\mathbf u_3}{\mathbf e_3}$

${\mathbf v} = {\mathbf v_1}{\mathbf e_1} + {\mathbf v_2}{\mathbf e_2} + {\mathbf v_3}{\mathbf e_3}$