Final answer:
Binormal vectors can differ at various points on a parabola without contradicting its planarity, while magnetic field lines cannot cross as that would imply non-unique field values at the intersection point.
Step-by-step explanation:
The question is focused on a property of cubic parabolas in mathematics and a misconception about magnetic field lines in physics. To find two points on a parabola where binormal vectors are different, we can select any two distinct points on the curve because the binormal vector varies with the curvature and torsion of the curve at each point. This variability does not contradict the fact that a cubic parabola is planar; all points, tangents, and normals lie in the same plane, which defines the curve as planar. However, the binormal vectors change because they are perpendicular to the osculating plane at each point on the curve.
Concerning the physics part, magnetic field lines should not cross each other because if they did, it would imply two different magnetic field directions at the point of intersection, which is impossible. A magnetic field at a point in space has a unique direction and magnitude, and if lines crossed, it would violate this principle.