http://thejuniverse.org/PUBLIC/LinearAlgebra/LOLA/planes/vect.html
As given in the first paragraph ,the plane formed by any two non collinear vectors passing through origin is shown but why will the plane extend to a very large space when the length of the vectors are fixed and how will we know whether the plane passes throughorigin or not?
It is assumed that you can take multiples of each of the two non-parallel direction vectors to generate the whole infinite two dimensional plane. The original two vectors as well as any sum of multiples will be entirely in the plane so if they start at the origin the plane will also contain the origin. We can specify a translation vector moving the plane away from the origin but still need to give two directional vectors to specify the plane.