Results 1 to 3 of 3

Math Help - Vectors : Image Of LIne

  1. #1
    Junior Member
    Joined
    May 2011
    Posts
    30

    Vectors : Image Of LIne

    Hi guys, got a question I need help in:

    Find, in the form r.n = d, the equation of the plane containing the points A,B and C whose position vectors are -i + j + k, i + 2j + 2k and 2i + 2j + 4k respectively.
    Find, in the form r = p + tq the equation of the image of the line r = -i + j + k + \lambda (i - 5k) reflected in this plane.

    I found the equation of the plane to be r = (-1, 1 ,1) + \lambda (1, 0, -5). But I don't know how to find the equation of the reflected line (L'). I know L' would definitely contain A but I will need the direction vector of the reflected line to form the equation, and to get the direction vector, I need at least one other point lying on L'. Any idea how to find the 2nd point?

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

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,318
    Thanks
    1232
    \displaystyle (-1, 1, 1) + \lambda (1, 0, -5) is not the equation of a plane, it's the vector form of a line.

    To find the equation of the plane, use your three points to create two vectors that lie in the plane. Take their cross product to find the normal to the plane. The equation of your plane \displaystyle ax + by + cz = d will have the same coefficients as your normal vector \displaystyle \textrm{n} = a\mathbf{i} + b\mathbf{j} + c\mathbf{k}. Then use one of the points in the plane to find \displaystyle d.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2011
    Posts
    30
    I think I type wrongly... sorry... the equation of the plane is r . (-2,3,1) = 6. I don't have problems finding the equation of the plane but I really don't know how to find the equation of the reflected line...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Image of line in complex plane
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 19th 2011, 07:48 AM
  2. Replies: 1
    Last Post: February 27th 2011, 03:02 AM
  3. Replies: 2
    Last Post: July 12th 2010, 08:34 AM
  4. span of image vectors
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 16th 2010, 04:01 AM
  5. Image of vectors when rotated
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 2nd 2009, 10:52 PM

Search Tags


/mathhelpforum @mathhelpforum