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**

Join Physics Forums Today!

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

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**