Assertion (A): Magnetic field lines around a bar magnet never intersect each other.

Reason (R): Magnetic field produced by a bar magnet is a quantity that has both magnitude and direction.

Both the Assertion and the Reason are true, and the Reason correctly explains the Assertion.

Assertion (A): The NCERT chapter explicitly states, "No two field-lines are found to cross each other. If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible." So A is true.

Reason (R): The chapter also explicitly states, "Magnetic field is a quantity that has both direction and magnitude." So R is true, since magnetic field is defined as a vector quantity.

Why R explains A: Because the magnetic field at any given point is a vector quantity, it can have only ONE unique direction at that point (the direction a compass north pole would point there). A field line represents this single direction of the field at every point along it. If two field lines were to intersect, the field at the point of intersection would have to point in two different directions simultaneously — which contradicts the fact that a vector quantity (having both magnitude AND a single definite direction) can only have one direction at a given point. Hence the vector nature of the magnetic field (Reason) is precisely why field lines never cross (Assertion), making R the correct explanation of A.