Answer
$-5\mathbf{i}+45\mathbf{j}$
Work Step by Step
Therefore, the value of $3\mathbf{v},4\mathbf{w}$ is,
$\begin{align}
& 3\mathbf{v}=\left[ 3\times \left( -3 \right) \right]\mathbf{i}+\left[ 3\times 7 \right]\mathbf{j} \\
& =-9\mathbf{i}+21\mathbf{j}
\end{align}$
$\begin{align}
& 4\mathbf{w}=\left[ 4\times \left( -1 \right) \right]\mathbf{i}+\left[ 4\times \left( -6 \right) \right]\mathbf{j} \\
& =-4\mathbf{i}-24\mathbf{j}
\end{align}$
Subtract $4\mathbf{w}$ from $3\mathbf{v}$ to get,
$\begin{align}
& 3\mathbf{v}-4\mathbf{w}=\left[ -9-\left( -4 \right) \right]\mathbf{i}+\left[ 21-\left( -24 \right) \right]\mathbf{j} \\
& =-5\mathbf{i}+45\mathbf{j}
\end{align}$
