Chapter 2.7, Problem 5CP

Use Multivariate Newton’s Method to find the two points in common of the three given spheres in three-dimensional space. (a) Each sphere has radius 1, with centers $(\text{1},\text{ 1},0)$, $\left(\text{1},0,\text{ 1}\right)$, and $\text{(0, 1, 1)}$ . (Ans. $\text{(1, 1, 1)}$ and $\text{(1/3, 1/3, 1/3))}$ (b) Each sphere has radius 5, with centers $\text{(1,-2,0)}$, $\text{(-2,2,-1)}$, and $\text{(4,-2,3)}$.