Question

why can't we show north and south to a point formed by the intersection of two magnetic field lines? [we know that 2 magnetic lines of force cannot intersect each other]

Answer 1

A magnetic field always must have a unique direction. Imagine you place a magmetic needle and it points in two different directions simultaneously. It is impossible for the magnetic needle to point in two directions, hence direction of magnetic field of a point must always be unique. That's the reason magnetic field lines do not intersect or touch each other