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16 years ago

Feb 8, 10:42 pm show options

Newsgroups: sci.math

From: snipped-for-privacy@gmail.com - Find messages by this author

Date: 8 Feb 2006 19:42:08 -0800

Local: Wed, Feb 8 2006 10:42 pm

Subject: unit vector is dimensionless, how to draw when coordinates for

length?

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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) ?

The issues gets even more muddled if we consider forces. Sometimes one

finds the unit vector of a position vector between two points (along a

rope or something) which has a force acting along it. The force vector

can then be determined by multiplying the unit vector by the magnitude

of the force. This obviously means that the unit vector is

dimensionless and can be used to bring about vectors with different

units into the same "x y z" frame. Anyone have an idea about what it

means to say a unit vector has length 1, with respect to thise

coordinate system (which measures lengths)? How can it be graphed in

this xyz frame?