Question

Знайдіть модуль вектора, a=-5b якщо b (-4;3)

Answer 1

А = -5b = -5*{-4;3} = {20;-15}.
модуль вектора а - это корень квадратный из суммы квадратов его координат :
$a = \sqrt{ {20}^{2} + { (- 15})^{2} } = \sqrt{400 + 225} = \sqrt{625} = 25$
ответ : |а| = 25.

Answer 2

To find the magnitude (or the length) of a vector, you can use the following formula:

|a| = sqrt(a_x^2 + a_y^2)

where a_x and a_y are the components of the vector "a."

Given that vector "a" is equal to -5 times vector "b," and the components of vector "b" are (-4, 3), we can find vector "a" as follows:

a = -5 * b a = -5 * (-4, 3)

Now, calculate the components of vector "a":

a_x = -5 * (-4) = 20 a_y = -5 * 3 = -15

Now, we can find the magnitude of vector "a":

|a| = sqrt(a_x^2 + a_y^2) |a| = sqrt(20^2 + (-15)^2) |a| = sqrt(400 + 225) |a| = sqrt(625) |a| = 25

So, the magnitude of vector "a" is 25.