Minimize dependence between vectors?

Question

Assume two $3D$ points namely $A$ and $B$ with coordinates $A=(A_x,A_y,A_z)$ and $B=(B_x,B_y,B_z)$. Let's say that $A_x,A_y,B_x,B_y$ are distributed uniformly on a disk with radius $R$ whereas $A_z$ and $B_z$ are fixed and not equal. As far as I am concerned, if $X$ is the vector from point $A$ to the origin and $Y$ is the vector from $A$ to $B$, $X$ and $Y$ lengths are dependent due to their common starting point $A$. Is there any case where the dependecy can me minimized so as to set $E[XY]$ almost equal to $E[X]E[Y]\;?$