Question

Даны точки M(-2;-4); К(-1;3); Р(4;4)Найти: 1) координаты векторов МК и РМ;2) модули векторов MK и PM.3) координаты вектора EF=2MK-3KP.Помогите бедному гуманитарию, прошу вас.

Answer 1

МК={-1-(-2); 3-(-4)}={1;7}

РМ={6;16}

модуль МК=√(-2-(-1))^2+(-4-3)^2(всё это выражение под корнем)=√1+49=√50

            РМ=√36+64=10

ЕF=2*√50-3*10=10√2+30

Answer 2

Calculating Vectors and Their Moduli

To find the requested information, we can follow these steps:

1. Coordinates of Vectors MK and RM: - The coordinates of vector MK can be found by subtracting the coordinates of point M from the coordinates of point K: - MK = (xK - xM, yK - yM) - Similarly, the coordinates of vector RM can be found by subtracting the coordinates of point M from the coordinates of point R: - RM = (xR - xM, yR - yM)

The coordinates of vectors MK and RM are: - MK = (-1 - (-2), 3 - (-4)) = (1, 7) - RM = (4 - (-2), 4 - (-4)) = (6, 8) 2. Moduli of Vectors MK and PM: - The modulus (or magnitude) of a vector can be calculated using the formula: - |v| = √(x^2 + y^2), where v = (x, y) - Using this formula, we can calculate the moduli of vectors MK and PM: - |MK| = √(1^2 + 7^2) = √(1 + 49) = √50 - |RM| = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 3. Coordinates of Vector EF = 2MK - 3KP: - To find the coordinates of vector EF, we can first calculate 2MK and 3KP separately and then subtract 3KP from 2MK: - 2MK = 2 * (1, 7) = (2, 14) - 3KP = 3 * (4, 4) = (12, 12) - EF = 2MK - 3KP = (2 - 12, 14 - 12) = (-10, 2)

Therefore, the requested information has been calculated as follows: 1. The coordinates of vectors MK and RM are (1, 7) and (6, 8) respectively. 2. The moduli of vectors MK and PM are √50 and 10 respectively. 3. The coordinates of vector EF = 2MK - 3KP are (-10, 2).