## Precalculus (6th Edition) Blitzer

Difference of two vectors is $\mathbf{v}-\mathbf{u}=\left( {{a}_{1}}-{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}-{{b}_{2}} \right)\mathbf{j}$.
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 the terms of $\mathbf{j}$ together and subtract the terms of $\mathbf{i}$ and $\mathbf{j}$, respectively. The resultant vector is the difference of 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 difference 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: Let the vectors $\mathbf{v}\text{ and }\mathbf{u}$ be 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}-\left( 7\mathbf{i}+2\mathbf{j} \right) \\ & =\left( 2\mathbf{i}-7\mathbf{i} \right)+\left( 6\mathbf{j}-2\mathbf{j} \right) \\ & =-5\mathbf{i}+4\mathbf{j} \end{align}