Hello I was doing some study for a maths test involving vectors when I came across this question:(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Vector Question

**Physics Forums | Science Articles, Homework Help, Discussion**