Answer
The required value is $3\text{v-4w}=\text{-23i}+\text{22j}$
Work Step by Step
We need:
$3\mathbf{v}-4\mathbf{w}$
And,
$\begin{align}
& \mathbf{v}=-5\mathbf{i}+2\mathbf{j} \\
& \mathbf{w}=2\mathbf{i}-4\mathbf{j}
\end{align}$
So,
$\begin{align}
& 3\text{v-4w}=\text{3}\left( \text{-5i}+\text{2i} \right)-\text{4}\left( \text{2i}-\text{4j} \right) \\
& =\left( -\text{15}-\text{8} \right)\text{i}+\left( \text{6}+\text{16} \right)\text{j} \\
& =\text{-23i}+\text{22j}
\end{align}$
So,
$3\text{v-4w}=\text{-23i}+\text{22j}$
Therefore, the required value is
$3\text{v-4w}=\text{-23i}+\text{22j}$.
