The vectors $\mathbf{v}=2\mathbf{i}-\mathbf{j}+5\mathbf{k}$ and $\ \mathbf{w}=3\mathbf{i}+\mathbf{j}-\mathbf{k}$ are orthogonal, since $$\mathbf{v}\,{\cdot}\, \mathbf{w}=6-1-5=0$$

Since $\mathbf{i}\,{\cdot}\, \mathbf{j}=1\,{\cdot}\, 0+ 0\,{\cdot}\, 1=0$, the standard basis vectors $\mathbf{i}$ and $\mathbf{j}$ in the plane are orthogonal. The standard basis vectors $\mathbf{i}$, $\mathbf{j}$, and $\mathbf{k}$ in space are mutually orthogonal, since $\mathbf{i}\,{\cdot}\, \mathbf{j}=0,$ $\mathbf{j}\,{\cdot}\, \mathbf{k}=0,$ and $\mathbf{k}\,{\cdot}\, \mathbf{i}=0.$