Answer
$3$
Work Step by Step
Find the scalar, $\mathbf{u}\cdot \left( \mathbf{v+w} \right)$ as,
$\begin{align}
& \mathbf{u}\cdot \left( \mathbf{v+w} \right)\mathbf{=}\left( 2\mathbf{i-j} \right)\cdot \left( 3\mathbf{i+j+i+}4\mathbf{j} \right) \\
& =\left( 2\mathbf{i-j} \right)\cdot \left( 4\mathbf{i+}5\mathbf{j} \right) \\
& =2\cdot 4+\left( -1 \right)\cdot 5 \\
& =8-5
\end{align}$
Solve further to get the result as,
$\begin{align}
& \mathbf{u}\cdot \left( \mathbf{v+w} \right)=8-5 \\
& =3
\end{align}$
Hence, the scalar of $\mathbf{u}\cdot \left( \mathbf{v+w} \right)$ is $3$.
