Answer
$35$
Work Step by Step
Find the scalar, $\left( 5\mathbf{v} \right)\cdot \mathbf{w}$ as,
$\begin{align}
& \left( 5\mathbf{v} \right)\cdot \mathbf{w=}\left[ 5\times \left( 3\mathbf{i+j} \right) \right]\cdot \left( \mathbf{i+}4\mathbf{j} \right) \\
& =\left( 15\mathbf{i}+5\mathbf{j} \right)\cdot \left( \mathbf{i+}4\mathbf{j} \right) \\
& =15\cdot 1+5\cdot 4 \\
& =15+20
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& \left( 5\mathbf{v} \right)\cdot \mathbf{w}=15+20 \\
& =35
\end{align}$
Hence, the scalar of $\left( 5\mathbf{v} \right)\cdot \mathbf{w}$ is $35$.
