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

[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?

 

[arildno]

Sure.

 

[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.

 

[CraigH]

It has to be defined. Usually the Euclidean metric is used, but others may be used.

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

 

[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.