Hello I was doing some study for a maths test involving vectors when I came across this question: For non zero vectors show that: |a-b|=|a+b| if and only if a and b are perpendicular. Deduce that a parallelogram is a rectangle if and only if its diagonals are equal in length. I did the first question using dot products: |a-b|=|a+b| |a-b|^2=|a+b|^2 (a-b).(a.b)=(a+b).(a+b) |a|^2+|b|^2-2|a||b|cosX=|a|^2+|b|^2+2|a||b|cosX -2|a||b|cosX=+2|a||b|cosX -cosX=cosX Therefore cosX=0 x=90, 270, 480.....etc. Thus vector a and vector b must be perpendicular for|a-b|=|a+b| to be valid. I'm not sure if this way is correct though.... Could someone please check if the stuff that I've done above is right? Also, could I get some help doing the second part of teh question? Thank you it will be much apprechiated.