Precalculus (6th Edition) Blitzer

Sum of two vectorsis $\mathbf{v}+\mathbf{u}=\left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j}$.
First, write the two vectors in terms of $\mathbf{i}\text{ and }\mathbf{j}$. Then, take the like terms together. This means that we take the terms of $\mathbf{i}$ together and terms of $\mathbf{j}$ together and then add the terms of $\mathbf{i}$ and $\mathbf{j}$, respectively. The resultant vector is the sum of the two vectors and it is given by $\mathbf{v}+\mathbf{u}$. If $\mathbf{v}={{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j}\text{ and }\mathbf{u}\text{=}{{a}_{2}}\mathbf{i}\text{+}{{b}_{2}}\mathbf{j}$, then the sum of two vectors is $\mathbf{v}+\mathbf{u}$. $\mathbf{v}+\mathbf{u}=\left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j}$ Example: Information: Consider that the vectors $\mathbf{v}\text{ and }\mathbf{u}$ are given as \begin{align} \mathbf{v}=2\mathbf{i}+6\mathbf{j} & \\ \mathbf{u}=7\mathbf{i}+2\mathbf{j} & \\ \end{align} Then, the sum of vectors $\mathbf{v}\text{ and }\mathbf{u}$ is given by $\mathbf{v}+\mathbf{u}$. \begin{align} & \mathbf{v}+\mathbf{u}=2\mathbf{i}+6\mathbf{j}+7\mathbf{i}+2\mathbf{j} \\ & =\left( 2\mathbf{i}+7\mathbf{i} \right)+\left( 6\mathbf{j}+2\mathbf{j} \right) \\ & =9\mathbf{i}+8\mathbf{j} \end{align}