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Find a vector orthogonal

  1. Sep 2, 2005 #1
    Find a vector orthogonal to both <-3,2,0> and to <0,2,2> of the form
    <1,_,_> (suppose to fill in the blanks)

    well i thought the cross product would do the trick, but i keep getting the wrong answer.
    I|2 0| - j |-3 0| + k |-3 2|
    |2 2| |0 2| |0 2|

    (format is kinda messed up, but im pretty sure you can tell how i had it set up)

    i(4-0) -j(-6-0)+ k(-6-0) = 4i+6j+6k = 2i+3j+6k


    so the answer should be <2,3,6> which is obviously incorrectly cause i dont even have a 1.
     
  2. jcsd
  3. Sep 2, 2005 #2
    assuming that's the correct answer, why don't you multiply by a scalar
     
  4. Sep 2, 2005 #3
    You're pretty much right, apart from the sloppy sign change that crept in towards the end for no reason (-6k not +6k). Is it specified in the question that all components must be integers? If not, I would suggest simply dividing your answer by 2.
     
  5. Sep 2, 2005 #4

    LeonhardEuler

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    Gold Member

    It can't be specified that the components are all integers because there is only one unique vector that is perpendicular to two non-colinear vectors, up to constant multiples. So dividing gives the unique answer to the problem.
     
  6. Sep 2, 2005 #5
    I suppose that I was being over cautious that I could have made some kind of mistake or overlooked something but you are right of course.
     
  7. Sep 2, 2005 #6
    thanks alot, dividing by 2 worked. i had the -6 in on my paper, but when i typed it on here, everything was messed up including the answer i gave at the end. i was really sleepy awhile i was typing it, thanks agian for the help
     
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