Let `sigma_1,sigma_2,sigma_3` be planes passing through the origin. Assume that `sigma_1` is perpendicular to the vector (1,1,1), `sigma_2` is perpendicular to a vector (a,b,c) and `sigma_3` is perpendicular to the vector `(a^2,b^2,c^2)`. What are all the positive values of a,b and c so that `sigma_1capsigma_2capsigma_3` is a single point?

Options

A. Any positive value of a,b, and c other than 1
B. Any positive values of a,b and c where either `a!=b,b!=c` or `a!=c`
C. Any three distinct positive values of a,b and c
D. There exist no such positive real numbers a,b,and c