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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} $
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