# 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.