с решением 14 (а). В ответе написано (-∞ ; -3]U[-8/3;0]U{-(8^(1/2)); 8^(1/2)}. Не пойму, откуда интервал взялся.

Robotics experts predict that it will not be too long before robots become an ordinary part of most households. In my opinion, the presence of robots in homes will be a wonderful thing.

First of all, robots will be able to do all the chores around the house. For example, they will be able to do the cleaning, the cooking, and maybe even the shopping. As a result, families will be able to spend more quality time together.

Secondly, robots will be able to act as carers. For instance, they will be able to babysit children and look after the elderly. Consequently, families will not need to spend extra money on expensive home help, so they will have more money to improve their lives.

On the other hand, people may come to depend on robots too much. This means that if their robot stops working they may find it especially difficult or tiring to do even the simplest of tasks.

All in all, it seems to me that robots will be extremely useful around the house, but no matter how helpful they may be, we should not rely on them completely.

Если прямая перпендикулярно плоскости, то ее направляющий вектор является нормальным вектором плоскости.

1)Уравнение плоскости через нормальный вектор: , где A, B, C - координаты нормального вектора плоскости N(A,B,C).
Уравнение данной плоскости  ⇒ N(2,-3,4).

2)Уравнение прямой через точку направляющий вектор: , где  - координаты точки M(), через которую проходит прямая,  - координаты направляющего вектора S().
По условию S() = N(A,B,C) ⇒ N(2,-3,4) = S(2,-3,4); M(1,-2,3).

3)Готовое уравнение прямой: