Answer
$\mathbf{v}$ and $\mathbf{w}$ are not orthogonal.
Work Step by Step
Dot product of $\mathbf{v}$ and $\mathbf{w}$ can be obtained as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=\left( 2\mathbf{i}-2\mathbf{j} \right)\cdot \left( -\mathbf{i}+\mathbf{j} \right) \\
& =2\cdot \left( -1 \right)+\left( -2 \right)\cdot 1 \\
& =-2-2 \\
& =-4
\end{align}$
As the dot product of $\mathbf{v}$ and $\mathbf{w}$ is not zero, thus, $\mathbf{v}$ and $\mathbf{w}$ are not orthogonal.
Hence, $\mathbf{v}$ and $\mathbf{w}$ are not orthogonal.
