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Topic: difference between a vector and a point (in R^n)
Replies: 12   Last Post: Sep 2, 2013 7:41 PM

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 J.B. Wood Posts: 46 Registered: 8/29/06
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 3-D 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 3-D 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 3-D space may have components that are phasors. For
example, a 3-D 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 e-mail: arl_123234@hotmail.com