Results 1 to 2 of 2

Math Help - Vector: Lines Intersect

  1. #1
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1

    Vector: Lines Intersect

    Vectors have to be my weakest points. How would I do this question, will I need to find s and t? Help would be appreciated.

    _______________________________________________


    Q:

    Referred to a fixed origin O, the lines l_1 and l_2 have equations \bold r = 3 \bold i + 6 \bold j + \bold k + s (2 \bold i + 3 \bold j - \bold k) and \bold r = 3 \bold i - \bold j + 4 \bold k + t ( \bold i -2 \bold j + \bold k) respectively, where s and t are scalar parameters.

    Show that l_1 and l_2 intersect and determine the position vector of their point of intersection.


    _______________________________________________

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Rewrite the lines as: l_1  = \left\{ \begin{array}{r}<br />
 3 + 2s \\ <br />
 6 + 3s \\ <br />
 1 - s \\ <br />
 \end{array} \right.\quad ,\quad l_2  = \left\{ \begin{array}{r}<br />
 3 + t \\ <br />
  - 1 - 2t \\ <br />
 4 + t \\ <br />
 \end{array} \right.
    Now just solve the system.
    But make sure the the solution works for all three equations.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Show that the two lines do not intersect.
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 30th 2011, 08:20 AM
  2. Replies: 0
    Last Post: October 9th 2010, 01:28 PM
  3. Do these lines intersect? If so...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 8th 2010, 12:48 PM
  4. Replies: 2
    Last Post: March 17th 2009, 07:52 AM
  5. Matrices: 2 lines intersect
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 14th 2008, 01:02 PM

Search Tags


/mathhelpforum @mathhelpforum