How do we decide the direction of vector, that is orthogonal to some other vector? assume that two vector given with relationship below: $$\vec{n}\cdot \vec{u} = 0 $$ Then $\vec{n}$ and $\vec{u}$ are orthogonal vectors. Assume that we now have the direction of $\vec{n}$ 
Then there are infinitely many possible direction for $\vec{u}$

How do we choose the vector $\vec{u}$?
When we consider vector valued functions, we choose Normal vector to be directed inner side of the curve.
When we consider grad $\nabla$ we know that it is perpendicular to any level curve. Then we choose $\nabla$ to be directed towards outward of the curve.
How do we decide direction? What is the algorithm behind that? What am I missing? Or is it application dependent?

There is a special case for twice-differentiable curves acting in $R^3$ For any point of such a curve you can explicitly define an orthonormal basis in $R^3$ that includes the normalized direction and two orthonormal vectors.
The trick is to realize that if $f''$ exists and is and not zero
$(f'(t) \cdot f'(t))' = 0 =  2f''(t)\cdot f'(t) = 0$
and it follows that
$(\frac{f'(t)}{||f'(t)||}, \frac{f''(t)}{||f''(t)||}, \frac{f'(t)}{||f'(t)||} \times \frac{f''(t)}{||f''(t)||})$ 
is an orthonormal basis in $R^3$.
