Re: unit vector of a length(position vector) graphed in length based axes?


Timo Nieminen wrote:
On Fri, 9 Feb 2006 i.love.jeevitha@xxxxxxxxx wrote:

Timo Nieminen wrote:
On Thu, 8 Feb 2006 i.love.jeevitha@xxxxxxxxx wrote:

Positoin vector is just the vector representing the position of some
point relative to the other (example, if a cube has a side length of
3m, the position vector representing one of the diagonals would be
(3m,3m,3m) - the unit vector associated with this position vector would
be (1,1,1) -dimensionless) How would i think about this unit vector on
the same length-based axes where the cube is drawn?

Your length-based axes are not dimensionless, your unit vector is. Given a
2D graph with length-based axes, where would you locate (3,$2000)?

What does it mean
that the unit vector has magnitude 1?

Your unit vector is pure direction; to make it mean something in your
chosen coordinate system, multiply it by a magnitude with the same
dimensions as your axes.

So the unit vector in this situation really doesnt' have a magnitude.
So one cannot draw it by itself on these axes?

It doesn't have a meaningful length on those axes. You can always
arbitrarily choose a length, so thaat the drawing looks OK. It would just
be an arrow of whatever length you choose, just indicating a direction.


Makes sense thanks.

I also have a follow up. Say one wants to find the scalar projection
of a F onto a position(length based) vector. Essentially, trying to
find the component of that force in the direction of the position
vector (which could represent a rope for instance).

proj = F dot r
----------
r dot r

The units turn out to be = N/m. The book I'm self studying about
doesn't mention units or anything in this case, but says the results it
the component of the force in the direction of the position vector. It
make sense, EXCEPT when one considers the units involved. N/m ??
Should I just disregard this and take it for what it is? Is there a
mathematical explanation that doesn't lead to this odd result?

Thank you so much Mr Nieminen

.

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