Re: unit vector of length vector is dimensionless???

i.love.jeevitha@xxxxxxxxx wrote in news:1139457792.835079.65320
@z14g2000cwz.googlegroups.com:



Say there are x, y, z coordinates set up for "some space" on earth,
where the coordinates represent lengths. Say the space is a
playground or a space around some buildings in downtown new york.


If there is a position vector between 2 points in this space, say
between two buildings or something, then the magnitude of this vector
is a length (metres, or whatever). That is the dimension of the
position vector or any vector which this coordinate system is really
set up for is length.


Now if we find the unit vector of the said position vector, it is
dimensionless. How would one graph the unit vector on this coordinate
system? How would one go about "thinking" about what it really means
to say that this unit vector has magnitude 1? Is that 1m? No. Then what

is it (geometrically) ?


It is called the direction cosine of the position vector. It has all sorts
of uses in mechanics, none of which I can remember. It is the normalised
direction information of that vector and is the complement (in a non
mathematical sense) of the magnitude of the vector.

Cheers

Greg
.

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