Recall u*u = ||u||^2
||a +b|| ^2 = (a+b)*(a+b) = ||a||^2 + 2a*b +||b||^2
what does this tell you?
Does it mean b=0?
first of all vectors cannot be positive or negative. and it makes no sense
to say things like a > b when and b are vectors.
secondly the point i wanted you to see is that
1. for both i + j and i - j |i+j|^2 = |i|^2 +|j|^2
2. i an j are perpindicular
3. If you graph the vectors notice that i , j and i+j form a right triangle
as does i,j, and i - j which is the point Captain Black was making when he asked you to consider a parallelogram
I think we were both trrying to get you to realize on your own with hints
then a and b are perpindicular period.