GROUP 12
Sphere-Sphere Collision
Group - 4 questions
Given the two spheres:
$S_{1}:(z-1)^{2}+(y-2)^{2}+(z-3)^{2}=9$ and $S_{2}:(z-5)^{2}+(y-5)^{2}+(z-3)^{2}=4$
Find the distance between the two sphere positions

Step 1 ：Given the two spheres: \(S_{1}:(z-1)^{2}+(y-2)^{2}+(z-3)^{2}=9\) and \(S_{2}:(z-5)^{2}+(y-5)^{2}+(z-3)^{2}=4\)

Step 2 ：The distance between two spheres (or more generally, any two points in 3D space) can be calculated using the Euclidean distance formula. The Euclidean distance between two points \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) is given by \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}\).

Step 3 ：From the equations of the spheres, we can see that the center of \(S_1\) is at \((1, 2, 3)\) and the center of \(S_2\) is at \((5, 5, 3)\). We can substitute these values into the Euclidean distance formula to find the distance between the two spheres.

Step 4 ：The distance between the two sphere positions is \(\boxed{5.0}\) units.