Answer
$12$
Work Step by Step
Find the scalar, $\mathbf{v}\cdot \left( \mathbf{u+w} \right)$ as,
$\begin{align}
& \mathbf{v}\cdot \left( \mathbf{u+w} \right)\mathbf{=}\left( 3\mathbf{i+j} \right)\cdot \left( 2\mathbf{i-j+i+}4\mathbf{j} \right) \\
& =\left( 3\mathbf{i}+\mathbf{j} \right)\cdot \left( 3\mathbf{i}+3\mathbf{j} \right) \\
& =3\cdot 3\mathbf{+}1\cdot 3 \\
& =9+3
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& \mathbf{v}\cdot \left( \mathbf{u+w} \right)=9+3 \\
& =12
\end{align}$
Hence, the scalar of $\mathbf{v}\cdot \left( \mathbf{u+w} \right)$ is $12$.
