What the formula for the distance from a point to a sphere

In summary, there is a formula for finding the distance from a point to a plane, which involves the coordinates of the point and the coefficients of the plane's equation. However, there is not a widely known formula for finding the distance from a point to a sphere. It is suggested to find the distance from the point to the center of the sphere and subtract the radius of the sphere, with a different approach for points inside the sphere.
  • #1
khdani
55
0
i know this formula from a point to a plane
[tex]
d=\frac{Ax_0+By_0+cz_0}{\sqrt{A^2+B^2+C^2}}
[/tex]

and i know that i could take from its center.

but i am looking for a formula of the distance from a point to a sphere
??
 
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  • #2
I'm not aware that there is such a formula, at least not one that is widely circulated. Assuming the point is outside the sphere, find the distance from the point to the center of the sphere, and then subtract the radius of the sphere.
 
  • #3
If the point is inside the sphere, do the subtraction the other way around. Or, like you do with the distance between two points on a number line, do the subtraction either way and take the absolute value.
 

1. What is the formula for the distance from a point to a sphere?

The formula for calculating the distance from a point to a sphere is:

d = |r - c| - r

Where d is the distance, r is the radius of the sphere, and c is the center of the sphere.

2. How is the distance from a point to a sphere calculated?

The distance from a point to a sphere is calculated by finding the difference between the distance from the point to the center of the sphere and the radius of the sphere.

3. Can the distance from a point to a sphere be negative?

No, the distance from a point to a sphere cannot be negative. It is always a positive value.

4. Is there a special formula for finding the distance from a point to a sphere?

Yes, there is a specific formula for finding the distance from a point to a sphere, as mentioned in the first question. This formula takes into account the radius and center of the sphere.

5. What is the significance of the distance from a point to a sphere?

The distance from a point to a sphere is important in various fields such as mathematics, physics, and engineering. It is used to determine the closest distance between a point and a spherical object, which can help in solving various problems and equations.

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