Compute the largest possible distance between two points A and B, where A is a point on the sphere of radius 19 with center (-2, -10, 5) and B is a point on the sphere of radius 87 with center (12, 8, -16).
I have a hunch it is the distance between the two centers +19 + 87
To compute the largest possible distance between two points A and B, we need to find the sum of the radii of the spheres centered at A and B.
Let's start by finding the distance between the centers of the two spheres, given that the center of sphere A is (-2, -10, 5) and the center of sphere B is (12, 8, -16).
To calculate the distance between two points in three-dimensional space, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points. In this case, let A be (x1, y1, z1) and B be (x2, y2, z2).
So, the distance between the centers of the two spheres is:
d = √((12 - (-2))^2 + (8 - (-10))^2 + (-16 - 5)^2)
Simplifying:
d = √((14)^2 + (18)^2 + (-21)^2)
Now, we can calculate the sum of the radii of the two spheres:
Sum of radii = 19 + 87
Finally, the largest possible distance between points A and B is the sum of the radii plus the distance between the center points:
Largest possible distance = sum of radii + distance between center points
Largest possible distance = (19 + 87) + √((14)^2 + (18)^2 + (-21)^2)
This expression can be evaluated to get the final answer.