Answer
Two vectors are orthogonal if the dot product of both the vectors is 0.
Work Step by Step
If $v$ and $w$ are non-zero vectors and $\theta $ is the smallest non-negative angle between $\mathbf{u}$ and $\mathbf{w}$,
Then the angle between two vectors can be calculated as:
$\begin{align}
& \cos \theta =\frac{\mathbf{u}\centerdot \mathbf{w}}{\left\| \mathbf{u} \right\|\left\| \mathbf{w} \right\|} \\
& \mathbf{u}\centerdot \mathbf{w}=\left\| \mathbf{u} \right\|\left\| \mathbf{w} \right\|\cos \theta \\
\end{align}$
Two vectors are said to be orthogonal if the angle between them is ${{90}^{\circ }}$
If $\mathbf{u}$ and $\mathbf{w}$ are orthogonal then,
$\begin{align}
& \mathbf{u}\centerdot \mathbf{w}=\left\| \mathbf{u} \right\|\left\| \mathbf{w} \right\|\cos 90{}^\circ \\
& =\left\| \mathbf{u} \right\|\left\| \mathbf{w} \right\|\left( 0 \right) \\
& =0
\end{align}$
$\mathbf{u}\centerdot \mathbf{w}=0$
