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What is the notation for the distance between two position vectors?

  1. Nov 5, 2013 #1
    If I have two 3 dimensional position vectors:


    What is the notation for the distance between them?

    I know to calculate the distance I would use:

    r = SQRT ( (s1-v1)^2 + (s2-v2)^2 + (s3-v3)^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. jcsd
  3. Nov 5, 2013 #2


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  4. Nov 5, 2013 #3


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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.
  5. Nov 5, 2013 #4
    Hi mathman,
    Thanks for the answer. What do you mean when you say it has to be defined?
  6. Nov 6, 2013 #5


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    Let v = (x,y,z)

    Definition 1: ||v|| = (x2 + y2 + z2)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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