A vector in the Cartesian coordinate can be written as:
A = axAx + ayAy + azAz
The differential length in the Cartesian coordinate is given by:
dl = axdx + aydy + azdz
The differential area of each side in Cartesian coordinate is given by:
dsx = dy ∙ dz
dsy = dx ∙ dz
dsz = dx ∙ dy
The differential volume in the Cartesian coordinate is given by:
dv = dx ∙ dy ∙ dz