Answer
$12$
Work Step by Step
Find the scalar, $\mathbf{u}\cdot \mathbf{v}+\mathbf{u}\cdot \mathbf{w}$ as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{u}+\mathbf{v}\cdot \mathbf{w=}\left( 3\mathbf{i+j} \right)\cdot \left( 2\mathbf{i-j} \right)+\left( 3\mathbf{i+j} \right)\cdot \left( \mathbf{i+}4\mathbf{j} \right) \\
& =3\cdot 2+1\cdot \left( -1 \right)+3\cdot 1+1\cdot 4 \\
& =6-1+3+4 \\
& =12
\end{align}$
Hence, the scalar of $\mathbf{v}\cdot \mathbf{u}+\mathbf{v}\cdot \mathbf{w}$ is $12$.
