vector addition

Adding two vectors component by component.

Vector addition combines $\mathbf u = (u_1,u_2)$ and $\mathbf v = (v_1,v_2)$ component-wise: $\mathbf u + \mathbf v = (u_1+v_1,\ u_2+v_2)$ . Geometrically, placing $\mathbf v$ 's tail at $\mathbf u$ 's tip and drawing the arrow from the origin to $\mathbf v$ 's new tip gives the same sum as the other order — both orderings trace two sides of the same parallelogram, whose diagonal is $\mathbf u + \mathbf v$ . Vector subtraction, $\mathbf u - \mathbf v$ , means $\mathbf u + (-1)\mathbf v$ .