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Equation of a line perpendicular to two vectors

  1. Dec 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the parametric and symmetric equations for the line through the point (2,1,0) and perpendicular to both <1,1,0> and <0,1,1,>

    2. Relevant equations
    Parametric equ:
    x = x_0 + at
    y = y_0 + bt
    z = z_0 + ct

    3. The attempt at a solution
    Cross product of <1,1,0> and <0,1,1> = <1,-1,1> = <a,b,c>

    Parametric equation:
    x = 2 + t
    y = 1 - t
    z = t

    Symmetric equation:
    x-2 = y-1 = z

    I'm not sure if I did this correctly. Is the cross product of the two vectors <a,b,c>?
  2. jcsd
  3. Dec 8, 2009 #2


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    Science Advisor
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    Gold Member

    Looks pretty much OK. Your cross product and parametric equations are correct. Check your signs on the symmetric version.
  4. Dec 8, 2009 #3
    Thanks for catching that.
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