# 3D Vector with homogeneous component

#### Nforce

I know that a 3D Vector is represent with three coordinates. For example $$\displaystyle V = [3, 2, 5]$$.

But I don't understand what a 3D vector with homogeneous component is. Does that extra component effect on the norm of a 3D vector? Or is the norm still $$\displaystyle | V | = \sqrt{3^2 + 2^2 + 5^2}$$?

Thank you for some explanation.

#### chiro

MHF Helper
Hey Nforce.

The definition of homogenous (like everything really) is different depending on who is defining it. In many mathematical contexts it refers to something involving a zero but I'm not sure what it means for your situation.

The norm of a vector should have the same definition for every vector in that space.

I am taking a look at this:

Homogeneous coordinates - Wikipedia, the free encyclopedia

and it says that homogenous co-ordinates refer to co-ordinates based on a projective space.

In a projective space, you don't have the same norm that you do in a Cartesian space: they are different kinds of spaces and subsequently they have different kinds of metrics, norms, and inner products (if these things exist for that space).

#### Nforce

So how can you calculate the norm then? Can you give me some example of a 3D vector with homogenous component and the norm for this 3d vector?

#### chiro

MHF Helper
Just to clarify though, are you talking about projective co-ordinate systems?

yes.