# 3D Vector with homogeneous component

• Oct 28th 2012, 10:17 AM
Nforce
3D Vector with homogeneous component
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.
• Oct 28th 2012, 06:12 PM
chiro
Re: 3D Vector with homogeneous component
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).
• Oct 28th 2012, 10:58 PM
Nforce
Re: 3D Vector with homogeneous component
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?
• Oct 28th 2012, 11:53 PM
chiro
Re: 3D Vector with homogeneous component
Just to clarify though, are you talking about projective co-ordinate systems?
• Oct 29th 2012, 11:18 AM
Nforce
Re: 3D Vector with homogeneous component
yes.