Question

If r=[x,y,z] and r0=[x0,y0,z0], describe the set of all points (x,y,z) such that Ir-r0I =1.

Answer 1

The points (x,y,z) that respond to Ir-r0I =1, are all that describes the form
`(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=1` with:

-1+x₀<x<1+x₀

-1+y₀<y<1+y₀

-1+z₀<z<1+z₀

Explanation:

All points required in this problem came from applying the definition of modulus of a vector:

Ir-r0I =1.

`|(x,y,z)-(x_(0),y_(0),z_(0))|=|(x-x_(0),y-y_(0),z-z_(0))|=\sqrt{(x-x_(0))^2+(y-y_(0))^2+(z-z_(0))^2}=1\\(x-x_(0))^2+(y-y_(0))^2+(z-z_(0))^2=1^2=1`