Question

Даны точка а(3;-1) и вектор а(4;8).при каких кординатах точки в ветор ав 1) равен вектору а 2) противоположен вектору а?

Answer 1

Это точный ответ, думаю что помогла     1) АВ=в(3;-3)
А(х;у), 3-х=3, х=0
-2-у=-3, у=1, А(0;1)
2) 3-х=-3, х=6
-2-у=3, у=-5, А(6;-5)

Answer 2

Given Information:

We are given a point A(3, -1) and a vector a(4, 8). We need to find the coordinates of a point B such that the vector AB + a = -a.

Solution:

To find the coordinates of point B, we need to subtract vector a from point A and equate it to the negative of vector a.

Let's denote the coordinates of point B as (x, y).

The vector AB can be calculated by subtracting the coordinates of point A from the coordinates of point B:

AB = (x - 3, y + 1)

According to the given condition, AB + a = -a. Substituting the values, we get:

(x - 3, y + 1) + (4, 8) = -(4, 8)

Simplifying the equation, we have:

(x - 3 + 4, y + 1 + 8) = (-4, -8)

(x + 1, y + 9) = (-4, -8)

Equating the corresponding coordinates, we get two equations:

x + 1 = -4 y + 9 = -8

Solving these equations, we find:

x = -5 y = -17

Therefore, the coordinates of point B are (-5, -17).

Answer: The coordinates of point B such that the vector AB + a is equal to the negative of vector a are (-5, -17).