Let us define the length of a vector a i +b j +c k as |a|+|b|+|c| . This definition coincides with the usual definition of length of a vector a i +b j +c k , iff

Step-by-step solution

We have, |a i +b j +c k |=|a|+|b|+|c| a^2+b^2+c^2 =|a|+|b|+|c| a^2+b^2+c^2=a^2+b^2+c^2+2(|a||b|+|b||c|+|c||a|) |a||b|+|b||c|+|c||a|=0 . a b=b c=c a=0 Any two of a, b and c are zero.