The distance between vectors is $d(x,y)=\|x-y\|$. It is symmetric, nonnegative, zero exactly when $x=y$, and satisfies $d(x,z)\le d(x,y)+d(y,z)$. For $(1,2)$ and $(4,6)$, the distance is $\sqrt{3^2+4^2}=5$.
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