2. Explain why the magnetic field would not be unique (that is, not have a single value) at a point in space where magnetic field lines might cross. (Consider the direction of the field at such a point.)

Magnetic field would not be unique at a point where they cross each other because the magnetic field will seem to have two different directions which is not possible. The magnetic field lines at any point in space are tangential to the direction of the magnetic field. As a result magnetic field lines are tangents to the magnetic field. When two magnetic field lines intersect, there will be two directions for the same magnetic field at the point of intersection which is impossible. As a result the magnetic field cannot be unique if this were possible.

no. dot product   =0 when vecs at right angles

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.