What can you conclude about a and b given that
(a) $\displaystyle ||a||^2+||b||^2=||a+b||^2$
(b)$\displaystyle ||a||^2+||b||^2=||a-b||^2$
I just do not like these open ended questions...I am never sure where to begin.
Does it mean b=0?
or a>b?
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
If
a)
(b)
then a and b are perpindicular period.