Originally Posted by **werehk** I just read a book which talks about vector differentiation. There are words like binormal,principal normal,torsion, curvature actually I don't understand why vectors can be differentiated.Could anyone explain a bit,please?
I only know that for curves, they can be differentiated to have their tangents plotted as a new graph, but for vectors in physics, they are in three dimensional, what are the physical meanings? Vectors can be differentiated so does it mean that vectors are like some curves? |

Vectors are quantities in a given direction. Typically in Physics we use them in association with a given coordinate system so we can decompose the vector into components in the directions of the coordinate axes.

In 3D space there are three coordinate directions so the vectors have three components. Typically these components depend on time, so we have for a vector v(t):

$\displaystyle \bold{v}(t) = \left ( \begin{matrix} x(t) \\ y(t) \\ z(t) \end{matrix} \right )$

Torsion and curvature are properties of curves in 3D space. I'm not sure what a "binomial principle norm" is. (But there are any number of ways you can define a measure of "distance," all of which have different properties. It is likely one of these. If you would like to know more about this and you have some knowledge of linear vector spaces, look up what a metric tensor is.)

-Dan