If $\vec{r}(t) = x(t) i + y(t) j$ be a simple curve C in the domain of a continuous vector field $\vec{F} = F_1 i + F_2 j + F_3 k$. If $\hat{n}$ is the outward pointing unit normal vector to the curve C then the flux accross the plane curve C is given by $= \int_{C} \vec{F} . \hat{n} dS$
Now if is given in my book that
$\hat{n} = \hat{T} \times \hat{k}$ ( if curve is moving in counter clockwise direction)
And
$\hat{n} = \hat{k} \times \hat{T}$ (if curve is moving in clockwise direction)
$( \hat{T}$ is unit tangent vector to the curve$.)$
I didn't understand the direction of $\hat{n}$. I know, it is a unit vector normal to the curve, but why it is represented by cross product of $\hat{T}$ and $\hat{k} ?$