For two vectors A and B. A+B =A-B, if and only if??​

if and only if is a zero vector.

Explanation:

An equation is true if and only if adding the same value to both sides of the equation (the value needs to be compatible) gives an equation that is also true.

Start with the .

This equation is true if and only if ( is added to both sides of the original equation.)

Vector addition and subtraction are associative. Therefore, if and only if , which is equivalent to .

if and only if (is added to both sides of this equation,) which is equivalent to .

if and only , which is equivalent to . That is: is the zero vector.

In other words:

.

Hence, if and only if is the zero vector.

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.