Answer
$35$
Work Step by Step
Find the scalar, $5\left( \mathbf{v}\cdot \mathbf{w} \right)$ as,
$\begin{align}
& 5\left( \mathbf{v}\cdot \mathbf{w} \right)\mathbf{=}5\left[ \left( 3\mathbf{i+j} \right)\cdot \left( \mathbf{i+}4\mathbf{j} \right) \right] \\
& =5\left[ 3\cdot 1+1\cdot 4 \right] \\
& =5\left( 3+4 \right) \\
& =5\times 7
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& 5\left( \mathbf{v}\cdot \mathbf{w} \right)=5\times 7 \\
& =35
\end{align}$
