Can two magnetic field lines intersect each other when the magnets are perpendicular to each other? can two magnetic lines intersect each other when the magnets are perpendicular to each other? The magnetic lines would be produced by electricity.
 A: 
can two magnetic lines intersect each other when the magnets are
  perpendicular to each other?

No, not in the sort of examples you're talking about anyway. Let me give you a real world example:

This is a topographical map. Do you see the brown lines? The represent locations of equal altitude. They don't exist, they're just lines on a map You won't see a brown line on the ground if you go there, nor do you expect to!
Now, do you see any of the lines crossing? Think about it for a second: if the lines crossed, that would mean that that spot on the ground has two different altitudes at the same time! That's not a thing. And what about the points between the lines, do they have no altitude? No, they're just not labelled.
Magnetic field lines are like these lines, they are not "real things", they are just a way of diagramming that makes it easier to understand. For topo maps we're making lines where the altitude is the same, for magnets, we're making lines where the magnetic field is the same.
Now I know what you're about to say... "but what about this:"

They look awfully real, don't they? But it's an illusion. Sprinkle the iron five times and you'll get five different patterns. They will be similar, but not the same. That's because they're not actually following some magic line in space, they're just getting magnetized and sticking to each other, it's a totally random process.
A: It is difficult to picture your magnet setup, but in certain cases, field lines may cross. Well, not really cross, but reach the same point. It is called magnetic reconnection and occurs in a range of effects in astrophysics or in laboratory plasma physics.
A: Magnetic field lines are vectors. You simply add the vector of each source of the magnetic field at that point and you have the direction and magnitude of the field at that point.
A: no, the magnetic field linas can never intersect each other
as if they intersect they have 2velocity components  at a single point which is not possible 
