Question

Будут ли векторы сонапрраленны c{2;-1;4}; d{4;-2;8}​

Answer 1

Да.

Пошаговое объяснение:

Рассчертив данные линии на координатной прямой, мы увидим их параллельность.

Answer 2

Для того чтобы определить, являются ли векторы c{2;-1;4} и d{4;-2;8} сонаправленными, нужно проверить, равны ли их координатные отношения.

Сon't worry, I'll speak English!

To determine whether the vectors c{2;-1;4} and d{4;-2;8} are collinear, we need to check if their coordinate ratios are equal.

Two vectors are collinear if and only if their corresponding coordinate ratios are equal for all coordinates.

So let's check the coordinate ratios:

For the x-coordinate:
c_x = 2 , d_x = 4

The ratio of their x-coordinates is c_x / d_x = 2 / 4 = 1 / 2.


For the y-coordinate:
c_y = -1 , d_y = -2

The ratio of their y-coordinates is c_y / d_y = -1 / -2 = 1 / 2.


For the z-coordinate:
c_z = 4 , d_z = 8

The ratio of their z-coordinates is c_z / d_z = 4 / 8 = 1 / 2.


Since all the coordinate ratios are equal to 1 / 2, we can conclude that the vectors c{2;-1;4} and d{4;-2;8} are collinear or parallel.

In other words, they have the same direction, but they may have different magnitudes.

I hope this explanation helps you understand whether the given vectors are collinear or not! Please let me know if you have any further questions.