SOLUTION: Let p0 = (x0,y0,z0)and p = (x,y,z). Describe the set of all points (x,y,z) for which ||p-p0|| = 1.

Algebra ->  College  -> Linear Algebra -> SOLUTION: Let p0 = (x0,y0,z0)and p = (x,y,z). Describe the set of all points (x,y,z) for which ||p-p0|| = 1.      Log On


   

Question 105470This question is from textbook Elementary Linear Algebra
: Let p0 = (x0,y0,z0)and p = (x,y,z). Describe the set of all points (x,y,z) for which ||p-p0|| = 1. This question is from textbook Elementary Linear Algebra

Answer by wgunther(43) About Me  (Show Source):
You can put this solution on YOUR website!
We are concerened with the norm of the vector (x-x0, y-y0, z-z0) equaling 1. This happens when
sqrt%28%28x-x_0%29%5E2%2B%28y-y_0%29%5E2%2B%28z-z_0%29%5E2%29=1}
Square both sides
%28x-x_0%29%5E2%2B%28y-y_0%29%5E2%2B%28z-z_0%29%5E2=1
Which you will recgonize as a circle of radius one centered at (x0,y0,z0)