Answer
Sum of two vectorsis $\mathbf{v}+\mathbf{u}=\left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j}$.
Work Step by Step
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 $\mathbf{v}+\mathbf{u}$.
$\begin{align}
& \mathbf{v}+\mathbf{u}=2\mathbf{i}+6\mathbf{j}+7\mathbf{i}+2\mathbf{j} \\
& =\left( 2\mathbf{i}+7\mathbf{i} \right)+\left( 6\mathbf{j}+2\mathbf{j} \right) \\
& =9\mathbf{i}+8\mathbf{j}
\end{align}$
