Definition:Curvilinear Coordinate Surface/Unit Normal

Definition
Let $\QQ_i$ be a family of surfaces contributing towards a curvilinear coordinate system in $3$-space.

Let $q_i$ denote the constant identifying a specific curvilinear coordinate surface within $\QQ_i$.

Let $\mathbf a_i$ be a unit normal to such a curvilinear coordinate surface in the direction of increasing $q_i$.

Then $\mathbf a_i$ is the unit normal associated with $\QQ_i$