Results 1 to 4 of 4

Math Help - Equation of The Plane

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    24

    Equation of The Plane

    Find the equation of the plane (if it exists) containing the two lines:

    A) R1(t)= <1-t, t, 3+2t> ; R2(t)= <t, 1+t, 5-2t>

    B) R1(t)= <1+3t, -2t, -1+t> ; R2(t)= <6t,1-4t,3+2t>

    C) R1(t)= <t, 1+t, 5+t> ; R2(t)= <-2+t, t, 7-2t>


    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jffyx View Post
    Find the equation of the plane (if it exists) containing the two lines:

    A) R1(t)= <1-t, t, 3+2t> ; R2(t)= <t, 1+t, 5-2t>

    B) R1(t)= <1+3t, -2t, -1+t> ; R2(t)= <6t,1-4t,3+2t>

    C) R1(t)= <t, 1+t, 5+t> ; R2(t)= <-2+t, t, 7-2t>


    Thanks!
    Take the cross product of the vectors in the direction of each line to get a normal to the plane. Get a point in the plane by choosing a point on one of the lines.

    You should know how to get the equation of a plane in the form ax + by + cz = d when you have a point in the plane and a normal to the plane.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    24
    Quote Originally Posted by mr fantastic View Post
    Take the cross product of the vectors in the direction of each line to get a normal to the plane. Get a point in the plane by choosing a point on one of the lines.

    You should know how to get the equation of a plane in the form ax + by + cz = d when you have a point in the plane and a normal to the plane.
    Please explain how do you go about to get the vectors in the direction of each line and how do get a point by choosing a point on the line.

    Thanks again.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    There can be different situations

    1) the lines are parallel but not equal => one plane is containing the 2 lines
    Take one point on the first line, one point on the second line, form a vector with these 2 points and make the cross product of this vector with the direction vector of the lines
    This will give a normal vector to the plane

    2) the lines are parallel and equal => an infinite number of planes is containing the line

    3) the lines are secant (and not equal) => one plane is containing the 2 lines
    Make the cross product of the 2 direction vector of the lines
    This will give a normal vector to the plane, giving the form of its Cartesian equation
    Define the point which is on the 2 lines, this will give you a complete equation of the plane

    4) the lines are not parallel and not secant => no plane is containing the 2 lines

    You have first to define the status of the 3 cases you have to treat (1, 2, 3 or 4)

    Reminder : if you know a normal vector (a,b,c) to a plane then one Cartesian equation of the plane is ax+by+cz+d=0. To find d you have to chose one point on the plane.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 1st 2011, 07:57 PM
  2. Replies: 3
    Last Post: December 5th 2010, 05:46 PM
  3. Replies: 3
    Last Post: October 12th 2010, 05:06 AM
  4. Replies: 4
    Last Post: May 26th 2010, 10:48 AM
  5. Replies: 2
    Last Post: May 23rd 2010, 10:46 AM

Search Tags


/mathhelpforum @mathhelpforum