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Matrix question

  1. Sep 10, 2005 #1
    Hi,
    i need enlightenment on this question of mine.

    Suppose i have two lines, L and M.
    L and M intersect at point X.
    Then is X a cross product of L and M?

    I read this from a pdf on Multiple View Geometry.
    Here the link http://www.syseng.anu.edu.au/~hartley/Papers/CVPR99-tutorial/tut_4up.pdf
    the eqn is on pg 8 top right corner slide.

    Thanks in advance!
     
  2. jcsd
  3. Sep 11, 2005 #2

    TD

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    Homework Helper

    Yes, that is correct.

    For example, take the lines [itex]x + y + 1 = 0[/itex] and [itex]-x + 2y = 0[/itex] with vector representations (according to your pdf file) [itex]\left( {1,1,1} \right)[/itex] and [itex]\left( {-1,2,0} \right)[/itex].

    The cross product is [itex]\left( {1,1,1} \right) \times \left( { - 1,2,0} \right) = \left( {2,1, - 3} \right)[/itex]. Dividing by -3 to get the z-component to equal 1 gives the cartesian intersection point of [itex]\left( { - \frac{2}{3}, - \frac{1}{3}} \right)[/itex]
     
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