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Prove two vectors are perpendicular (2-D)

  1. Feb 5, 2010 #1
    Show that (ai+bj)and (-bi+aj) are perpendicular...

    im clueless on what to do ..any hints will be greatly apperciated
    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. jcsd
  3. Feb 5, 2010 #2
    help anyone?
  4. Feb 5, 2010 #3
    Construct a triangle with these vectors as his sides, and use trigonometry to prove that they have a right angle between them
  5. Feb 5, 2010 #4


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    Two vectors are perpendicular if their dot product is zero. For your case, the dot product is -ab+ab=0.
  6. Feb 6, 2010 #5
    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|=[itex]\sqrt{a^2+b^2}[/itex]), OB=(-b,a)|OB|[itex]\sqrt{a^2+b^2}[/itex] , then AB=(b+a,b-a)|AB|=[itex]\sqrt{(b+a)^2+(b-a)^2}[/itex]
    then I assumed it to be a right triangle and used pythagoras
    i.e and is easily shown [itex]|OB|^2+|OA|^2=|AB|^2[/itex] ..
    I hope this proof is right thanks
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