Question

Чи колінарні вектори якщо координати їх початків дорівнюють (2 8) і (1 4) а координати кінців (1дроб 2 і 2)і (1дроб 4 і 4) ​

Answer 1

Ответ:

Объяснение:

2/1=8/4;(1/2)/(1/4) не равна2/4

то вектори не колінеарні.

Answer 2

Колінарні вектори - це вектори, які лежать на одній прямій. Щоб перевірити, чи є два вектори колінарними, ми можемо порівняти їхні координати. Якщо вони мають пропорційні координати, то ці вектори є колінарними.

У даному випадку, ми маємо два вектори з початками у точках (2, 8) і (1, 4), і кінцями у точках (1#### Definition of Collinear Vectors Collinear vectors are vectors that lie on the same line or are parallel to each other. In other words, if two vectors are collinear, one can be obtained from the other by scaling it. Let's determine if the given vectors are collinear based on their coordinates.

Calculation of Direction Ratios

To determine if the vectors are collinear, we can calculate the direction ratios of the vectors. The direction ratios of a vector are the ratios of its components along the coordinate axes.

The direction ratios of a vector with initial coordinates (x1, y1) and terminal coordinates (x2, y2) are given by: Direction Ratio along x-axis (a) = x2 - x1 Direction Ratio along y-axis (b) = y2 - y1

Calculation for the Given Vectors

For the given vectors: Vector 1: Initial coordinates (2, 8) and terminal coordinates (1/2, 2) Vector 2: Initial coordinates (1, 4) and terminal coordinates (1/4, 4)

Let's calculate the direction ratios for both vectors.

Direction Ratios Calculation

For Vector 1: a1 = (1/2) - 2 = -3/2 b1 = 2 - 8 = -6

For Vector 2: a2 = (1/4) - 1 = -3/4 b2 = 4 - 4 = 0

Conclusion

The direction ratios for the given vectors are: Vector 1: (-3/2, -6) Vector 2: (-3/4, 0)

Since the direction ratios of the two vectors are not proportional, the vectors are not collinear. Therefore, the given vectors are not collinear.