# Euclidean metric of 3D space

For 3D Euclidean space, does the metric of space \begin{gather} \delta_{ij}=\mathbb{I}= \begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix} \end{gather} show that the unit vectors are orthogonal \begin{gather} \hat{e_i}\cdot\hat{e_j}=\delta_{ij} \end{gather}

or does the fact that the unit vectors are orthogonal dictate what the metric of space must be?

• Which came first, the chicken or the egg? – Willie Wong Apr 19 '18 at 16:03
• That's two ways of saying the same thing. – John Rennie Apr 19 '18 at 16:10