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.