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Vector help(Planes and normals)

  1. Feb 17, 2008 #1

    rock.freak667

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    Homework Helper

    1. The problem statement, all variables and given/known data
    With O as the origin, the points A,B,C have position vectors
    i,i+j,i+j+2k
    respectively, Find a vector equation of the common perpendicular of the lines AB and OC.
    Show that the shortest distance between the lines AB and OC is [itex]\frac{2}{5}\sqrt{5}[/itex]

    Find,in the form ax+by+c=d, an equation for the plane containing AB and the common perpendicular of the lines AB and OC.


    2. Relevant equations

    Vector formulae.

    3. The attempt at a solution
    OA=i
    OB=i+j
    OC=i+j+2k

    AB=AO+OB=j

    the direction of the common perpendicular is ABxOC = 2i-k

    But to get the vector equation I need a point on the line. How do I find that?

    (Also, I was never really taught how to do these sorts of vector problems, only ones at AS math level)
     
  2. jcsd
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