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Homework Help: Drawing a Collection Of vectors Satisfying Cross Products

  1. Sep 14, 2011 #1
    1. The problem statement, all variables and given/known data
    Given a = <1,2,3> and b = <1,-1,-1>, sketch the collection of all position vectors c satisfying a x b = a x c

    2. Relevant equations

    3. The attempt at a solution

    I've calculated a x b = <1,4,-3> and Defining c = <x,y,z> I found a x c = <2z-3y, z-3x, y-2x>. I want to come up with an algebraic representation of the vectors so I created the following system of equations

    1 = 2z - 3y
    4 = 3x - z
    -3 = y - 2x

    So x,y, and z that satisfy all three equations are a possible vector. I'm having trouble solving it, and I'm thinking I'm just going to get a single solution to this system If I do manage to solve it and it has a solution.

    Can you help?
  2. jcsd
  3. Sep 14, 2011 #2


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    Science Advisor
    Homework Helper

    You are doing fine so far, I think. But if you think you will get a single solution you are jumping to conclusions. Work out the solution to your system. a x c=a x (c+k*a) for any constant k. c can't possibly be unique.
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