Question

модуль вектора а = 13
модуль вектора b = 19.
| a + b | = 24.
Найдите | a-b |.
| |-Модуль

Answer 1

C помощью скалярных произведений:

|a+b|^2 = (a+b, a+b) = (a, a) + (b, b) + 2(a, b) = |a|^2 + |b|^2 + 2(a, b)

2(a, b) = |a+b|^2 - |a|^2 - |b|^2 = 24^2 - 19^2 - 13^2 = 46.

|a-b|^2 = (a-b, a-b) = (a, a) + (b, b) - 2(a, b) = |a|^2 + |b|^2 - 2(a, b) =
19^2 + 13^2 - 46 = 484.


|a-b| = sqrt(484) = 22.