I'm stuck at the properties of a 3d curve parametrized by arc length. My problem is given below.

We know that the binormal of a curve at a point is:

$\displaystyle b = n \times t$

where $\displaystyle b = $ binormal and $\displaystyle n$ is normal to the curve and $\displaystyle t$ is tangent.

So binormal is the cross product of normal and tangent at a point of a curve.

Now if $\displaystyle b = n \times t$ why's that $\displaystyle n = b \times t$ ? How do one prove this statement?

What properties of mathematics verify that $\displaystyle n = b \times t$? Is it possible to kindly help me answer this question?