
Re: difference between a vector and a point (in R^n)
Posted:
Aug 27, 2013 3:15 PM


On 08/26/2013 11:51 AM, lite.on.beta@gmail.com wrote: > What is the difference between a vector and a point? > Why are there two concepts? > > Wessel described complex numbers as "vectors" in some space like R^2. > Argand described complex numbers are "points" in some space like R^2. > > What's the difference? > > What's wrong with me saying "a vector is a point, and a point is a vector" ? > Hello. In some engineering disciplines such as electrical that deal with 3D space, a vector is any quantity characterized by magnitude and direction. The vector is often that associated with a particular vector field (e.g. electromagnetic field strength), and as such has a point of origin in 3D space, IOW a vector point function (the vector is "bound" to a particular point in space). Scalars that are complex numbers are called "phasors". Now to make things more complicated, vectors occurring in 3D space may have components that are phasors. For example, a 3D vector point function V(x,y,z) using cartesian (rectangular) coordinates and having orthogonal basis vectors ex, ey and ez would be represented as
V(x,y,z) = Vx(x,y,z)ex + Vy(x,y,x)ey + Vz(x,y,z)ez
where the components Vx, Vy and Vz may be phasors or any function of x,y,z. The function doesn't have to be linear in x,y and/or z. Sincerely,
 J. B. Wood email: arl_123234@hotmail.com

