Re: Unit vector
From my point of view, differential may be
always equal to zero only when the fuction is constant in the whole time domain. Differential is known to be the main part of the functions increase. It may be writtten the following way:
R = R(x,y,z) - function of 3 independent variables.
dy = R'(x)dx+R'
dy+R'(z)dz - differential of the function
Here R'(x),R'
,R'(z) denote the private derivatives of the functions taken on x,y,z respectively. If all the derivatives are zero, then the differential is zero as well.
If you use the unit vector (in my opinion unit vector means normalizing the initial vector by dividing on its length: ru = r / |r|, where |r|=sqrt(x^2+y^2+z^2)) nothing changes, therefore all the above results remain fair.
With respect,
Dmitrij