# Prove two vectors are perpendicular (2-D)

1. Feb 5, 2010

### rbnphlp

Show that (ai+bj)and (-bi+aj) are perpendicular...

im clueless on what to do ..any hints will be greatly apperciated
thanks
I know Im missing something really simple

Also the book has not yet introduced the scalar product so they want me to use some other way

Last edited: Feb 5, 2010
2. Feb 5, 2010

help anyone?

3. Feb 5, 2010

### elibj123

Construct a triangle with these vectors as his sides, and use trigonometry to prove that they have a right angle between them

4. Feb 5, 2010

### mathman

Two vectors are perpendicular if their dot product is zero. For your case, the dot product is -ab+ab=0.

5. Feb 6, 2010

### rbnphlp

Thanks both of you ..the book hasn't introduced scaler product yet so I don't think they wanted me to use that method ..

I drew a triangle .. OA=(a,b)(|OA|=$\sqrt{a^2+b^2}$), OB=(-b,a)|OB|$\sqrt{a^2+b^2}$ , then AB=(b+a,b-a)|AB|=$\sqrt{(b+a)^2+(b-a)^2}$
then I assumed it to be a right triangle and used pythagoras
i.e and is easily shown $|OB|^2+|OA|^2=|AB|^2$ ..
I hope this proof is right thanks