# Intersection of planes by forming 3d lines

If I have $n$ known planes (known normal vector and a point on a plane) that intersect each other in such a way so as to form closely located 3D lines, then

(1). To get a common single 3D line to represent these intersections via least square solutions approach, minimally how many planes should be intersected?

If i take profile view of planes, Red dots indicate the intersection lines (passing into the computer screen), so, i am looking for best line to be represented all of them.

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Mind if I ask why you added eigenvalues and svd tags? –  Shuhao Cao Jun 4 '13 at 23:49

@slinga Yes, basically we are looking for the equation of the line $\mathbf{x}=\mathbf{x}_0+t\mathbf{b}$ where $\mathbf{x}_0$ is the point, $\mathbf{b}$ is that vector. –  Shuhao Cao Jun 5 '13 at 13:35