Answer
The scalar is $25$.
Work Step by Step
The scalar $5\mathbf{u}\cdot \left( 3\mathbf{v-}4\mathbf{w} \right)$ can be obtained as,
$\begin{align}
& 5\mathbf{u}\cdot \left( 3\mathbf{v}-4\mathbf{w} \right)\mathbf{=}5\left( -\mathbf{i}+\mathbf{j} \right)\cdot \left[ 3\left( 3\mathbf{i}-2\mathbf{j} \right)-4\left( -5\mathbf{j} \right) \right] \\
& =\left( -5\mathbf{i}+5\mathbf{j} \right)\cdot \left( 9\mathbf{i}-6\mathbf{j}+20\mathbf{j} \right) \\
& =\left( -5\mathbf{i}+5\mathbf{j} \right)\cdot \left( 9\mathbf{i}+14\mathbf{j} \right) \\
& =\left( -5 \right)\cdot 9+5\cdot 14
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& 5\mathbf{u}\cdot \left( 3\mathbf{v}-4\mathbf{w} \right)=\left( -5 \right)\cdot 9+5\cdot 14 \\
& =-45+70 \\
& =25
\end{align}$
Hence, the scalar of $5\mathbf{u}\cdot \left( 3\mathbf{v}-4\mathbf{w} \right)$ is $25$.
