Question

Can magnetic lines of forces of two different magnets intersect

Answer 1

The thing to remember while answering this question is that tangent to each point on a magnetic line of force would tell us the direction of the magnetic filed on that particular point.

Now, if two magnetic lines of force intersect then there would be two tangents from the point of intersection (one for each line). Hence, on this point there would be two directions of the magnetic field. It means that when a compass is placed on this particular point then its needle's north pole would show a deflection in two directions at the same time; but practically this is impossible. Hence, we can say that two magnetic lines of force can never intersect each other.

Answer 2

If two magnetic lines of force intersect with each other than there would have been two directions of magnetic field at the point of intersection, which is not possible.