Question

Даны точки A(2:-2:0) В(-4:2:2). Принадлежат ли они сферес центром S(-2:1:3)и радиусом 3 ? Решить задачу

Answer 1

Вычисляй расстояние AS и BS по формуле.
AS=√((-2-2)²+(1-(-2))²+(3-0)²) = √(16+9+9)=√34≠3. Значит А не принадлежит сфере. Про В аналогично.

Answer 2

Problem Analysis

We are given two points, A(2,-2,0) and B(-4,2,2), and we need to determine if they belong to a sphere with center S(-2,1,3) and radius 3.

Solution

To determine if the points A and B belong to the sphere with center S and radius 3, we can calculate the distance between each point and the center of the sphere. If the distance is equal to the radius, then the point belongs to the sphere.

The distance between two points in 3D space can be calculated using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Let's calculate the distance between point A and the center S:

Distance_A = sqrt((2 - (-2))^2 + (-2 - 1)^2 + (0 - 3)^2)

Simplifying the equation:

Distance_A = sqrt(4^2 + (-3)^2 + (-3)^2) = sqrt(16 + 9 + 9) = sqrt(34)

Now let's calculate the distance between point B and the center S:

Distance_B = sqrt((-4 - (-2))^2 + (2 - 1)^2 + (2 - 3)^2)

Simplifying the equation:

Distance_B = sqrt((-2)^2 + 1^2 + (-1)^2) = sqrt(4 + 1 + 1) = sqrt(6)

Since the distance between point A and the center S is not equal to the radius (3), point A does not belong to the sphere. Similarly, the distance between point B and the center S is also not equal to the radius, so point B does not belong to the sphere either.

Therefore, neither point A nor point B belongs to the sphere with center S(-2,1,3) and radius 3.

Answer

The points A(2,-2,0) and B(-4,2,2) do not belong to the sphere with center S(-2,1,3) and radius 3.