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Re: unit vector is dimensionless, how to draw when coordinates for length?
Posted:
Feb 11, 2006 6:12 AM
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In article <1139635837.058503.258560@g14g2000cwa.googlegroups.com>,
<i.love.jeevitha@gmail.com> wrote:
> Shmuel (Seymour J.) Metz wrote:
> > In <1139526674.048419.21960@z14g2000cwz.googlegroups.com>, on
> > 02/09/2006
> > at 03:11 PM, kiru.sengal@gmail.com said:
> >
> > >A unit vector does not really have a magnitude.
> >
> > It does in Engineering and Physics. A 1cm unit vector does not have
> > the same magnitude as a 1" unit vector. In fact, you have to choose
> > your metric before the concept of "unit vector" even makes sense.
> >
> > >Normalizing any vector
> >
> > Is undefined until you have chosen units. Change your units and you
> > change your definition of normalized. Google for gauge invariance.
> >
>
> I think my problem is that I'm trying to learn Linear Algebra and Eng
> Mechanics at the same time, and out of a huge coincidence the chapters
> that mentioned unit vectors in both books I use came about the same
> time. This is what led me to the confusion. I talked to the
> engineering prof (I'm *sort of* going to his lectures, but not
> registered in his course or school) and he gave me a confusing (I think
> wrong) explanation. He took apart the unit vector (for different
> things, like Force, moment/torque, position) and got their cartesian
> component vectors. Then he tried to tell me that the i, j, k unit
> vectors that make up the unit vectors for the different types of
> vectors were different. "The i, j, k vectors for moment are different
> from the i,j,k vectors for force....... etc. etc."
>
> I think the "truth" is that these unit vectors (even the standard i,j,k
> or e1, e2, e3) are all dimensionless, but for engineering mechanics
> it's safe to assume otherwise (without getting wrong answers... and
> answers is what we care about in applied studies? right?).
>
You're right. Your engineering professor was wrong. The i,j,k unit
vectors for a given coordinate system are the same when expressing a
force vector or when expressing a torque vector or when expressing any
vector.
Bob
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