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