Spheres in three-dimensional space (3D)
Similar to the circles in the plane there are spheres in three-dimensional space.
A vector representation is also possible for spheres.
Like the circles, the cartesian equation of the sphere is derived from this.
- $r$ is the radius
- $M(x_M|y_M|z_M)$ is the center
Spheres in 3D have many similarities to the circles in the plane (2D). Since we are in space, there is also a z coordinate for the spheres.
Point on sphere: position of point and sphere
We also insert the point $P(x_0|y_0|z_0)$ in the front part of the sphere equation.
Now we distinguish 3 cases again. The result is
- $=r^2$: The point is on the sphere.
- $<r^2$: The point is inside the sphere.
- $>r^2$: The point is outside the sphere.