Question

Даны вектора a=(-4;-3;8) b=(4;-3;0). Найти координаты вектора с=а+4b и его длину

Answer 1

Ну. Сначала сделаем вектор 4b, умножив все его координаты на 4, получим:
4b (16; -12; 0)
Потом сделаем вектор с, сложив а и 4б. Получим:
С(12; -15; 8)
Длину вектора по формуле:
|с| = корень(12^2 + (-15)^2 + 8^2 = корень(144+225+64) = корень из 433 = 20,8

Answer 2

Calculating Vector c and Its Length

To find the coordinates of vector c and its length, we can use the formula: c = a + 4b. Let's calculate the coordinates of vector c and then find its length.

The given vectors are: a = (-4, -3, 8) b = (4, -3, 0)

Using the formula c = a + 4b, we can calculate the coordinates of vector c: c = (-4, -3, 8) + 4*(4, -3, 0) c = (-4, -3, 8) + (16, -12, 0) c = (-4 + 16, -3 - 12, 8 + 0) c = (12, -15, 8)

Now, let's find the length of vector c. The length of a vector v = (x, y, z) is given by the formula: ||v|| = sqrt(x^2 + y^2 + z^2).

Using this formula, the length of vector c is: ||c|| = sqrt(12^2 + (-15)^2 + 8^2) ||c|| = sqrt(144 + 225 + 64) ||c|| = sqrt(433) ||c|| = √433

So, the coordinates of vector c are (12, -15, 8) and its length is approximately equal to √433.