Re: [Phys-l] Motion in 1D, vectors and vector components

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

Regarding the suggestion in the message below that one uses (at least
early on) arrays instead of expressions like:
v = v_x e_x + v_y e_y + v_z e_z
as well as an earlier suggestion that one treat 1-D motion as 3-D motion
in which, for a given choice of basis vectors, two of the array elements
are always zero:
In Six Ideas, when Thomas Moore uses an array to represent a vector in
terms of a specified basis, he uses a column array.  He uses one of the
suggestions here where he considers 1-D motion to be motion in 3 D which
happens to occur along a line.  So, when he covers 1-D motion, all the
column vectors have two 0 elements and indeed and he expects students to
write the full column vector for every relevant variable in every
relevant solution to a 1-D problem.  One advantage to using column
vectors to represent vectors is that, when he gets to 3-D motion, a
vector equation, written in terms of column vectors, "looks like" the
corresponding set of three "scalar" equations to which, in a particular
basis, it is equivalent.  I estimate that he is in the ballpark of 95%
consistent with that notation where the occasional representation of a
vector as a row vector does occur.

Aside, regarding notation:  Thomas Moore uses a word for "unit vector"
that I have never seen used that way anywhere else; he calls a unit
vector a "directional".  In that context the word "directional" is a
noun.

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of Rauber, Joel
> Sent: Friday, August 17, 2007 2:54 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Motion in 1D, vectors and vector components
Some text removed.
> I'm warming to this idea (more for lack of any other).  I've never
> been
> particularly fond of writing vectors as
>
> (v_x,v_y,v_z)
>
> preferring unit vectors
> V = v_x e_x + v_y e_y + v_z e_z
>
> OTOH, most of my students come to me more familiar with the 1st
> version
> where the words "array element" are quite natural.
>
> So I'm warming to this idea as well.  I can start with the probably
> more
> familiar (v_x,v_y,v_z) and define an "array element", should be
> familiar
> to most of my students; then quickly segue to unit vector methods.
> _______________________________________
>
> So I have.
>
> Component vector ->  which except at the very beginning I'll call a
> "projection"
>
> And an "array element"
>
> __________________________________________
> __________________________________________