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

1. Nov 5, 2013

CraigH

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 ( (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. Nov 5, 2013

Sure.

3. Nov 5, 2013

mathman

||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. Nov 5, 2013

CraigH

Hi mathman,
Thanks for the answer. What do you mean when you say it has to be defined?

5. Nov 6, 2013

mathman

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.