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What is the notation for the distance between two position vectors? 
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#1
Nov513, 01:37 PM

P: 202

If I have two 3 dimensional position vectors:
s and v What is the notation for the distance between them? I know to calculate the distance I would use: r = SQRT ( (s1v1)^2 + (s2v2)^2 + (s3v3)^2 ) where s1 is the first element in the position vector s etc. What is an equation that represents this? Can I use the equation: r= ( s  v ) where x is the modulus function? 


#2
Nov513, 02:00 PM

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Sure.



#3
Nov513, 03:02 PM

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x is symbol used for the norm (modulus) of x. It has to be defined. Usually the Euclidean metric is used, but others may be used.



#4
Nov513, 03:43 PM

P: 202

What is the notation for the distance between two position vectors?
Thanks for the answer. What do you mean when you say it has to be defined? 


#5
Nov613, 05:46 PM

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P: 6,080

Let v = (x,y,z)
Definition 1: v = (x^{2} + y^{2} + z^{2})^{1/2} Definition 2: v = x + y + z Definition 3: v = max(x,y,z) There are endless possibilities, such as using nth power with nth root, analogous to Euclidean. 


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