Prove two vectors are perpendicular (2-D)

[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 I am missing something really simple

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

 

[rbnphlp]

help anyone?

 

[elibj123]

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

 

[mathman]

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

 

[rbnphlp]

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

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

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