Answer
$-3\mathbf{i}+12\mathbf{j}$
Work Step by Step
Addition and subtraction for the given vectors $\mathbf{v}={{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j}$ and $\mathbf{w}={{a}_{2}}\mathbf{i}+{{b}_{2}}\mathbf{j}$
is given by
$\begin{align}
& \mathbf{v}+\mathbf{w}=\left( {{a}_{1}}+{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\mathbf{j} \\
& \mathbf{v}-\mathbf{w}=\left( {{a}_{1}}-{{a}_{2}} \right)\mathbf{i}+\left( {{b}_{1}}-{{b}_{2}} \right)\mathbf{j} \\
\end{align}$
Here, ${{a}_{1}}=1,{{a}_{2}}=-2,{{b}_{1}}=-5,{{b}_{2}}=7$
So,
$\begin{align}
& \mathbf{w}-\mathbf{v}=\left( -2\mathbf{i}+7\mathbf{j} \right)-\left( \mathbf{i}-5\mathbf{j} \right) \\
& =\left( -2-1 \right)\mathbf{i}+\left[ 7-\left( -5 \right) \right]\mathbf{j} \\
& =-3\mathbf{i}+12\mathbf{j}
\end{align}$
Hence, the vector $\mathbf{w}-\mathbf{v}=-3\mathbf{i}+12\mathbf{j}$.
