Answer
$20$
Work Step by Step
Find the scalar, $\left( 4\mathbf{u} \right)\cdot \mathbf{v}$ as,
$\begin{align}
& \left( 4\mathbf{u} \right)\cdot \mathbf{v=}\left[ 4\times \left( 2\mathbf{i-j} \right) \right]\cdot \left( 3\mathbf{i+j} \right) \\
& =\left( 8\mathbf{i-}4\mathbf{j} \right)\cdot \left( 3\mathbf{i+j} \right) \\
& =8\cdot 3+\left( -4 \right)\cdot 1 \\
& =24-4
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& \left( 4\mathbf{u} \right)\cdot \mathbf{v}=24-4 \\
& =20
\end{align}$
Hence, the scalar of $\left( 4\mathbf{u} \right)\cdot \mathbf{v}$ is $20$.
