Results 1 to 6 of 6

Math Help - Equation of a plane in normal form ( with 2 lines)

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    83

    Equation of a plane in normal form ( with 2 lines)

    Hi
    Problem: a plane has got a straight line
    (x,y,z)= (5+t,6-t,7+2t) and is parallell with
    The line (x,y,z)= (3+t,5+t,6+t) determine the equation
    Of the plane in normal form


    We got two lines

    I can write line1 as
    (5,6,7) + t*(1,-1,2)

    Means a point 1 and vector 1

    The same applies for line2

    (3,6,5) + t(1,1,1)

    Point 2 and vector 2

    I have a feeling I have to use Sarrus rule on this
    Can someone show me how solve it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Equation of a plane in normal form ( with 2 lines)

    Hey Riazy.

    You can use the equations to get two direction vectors (remember the direction is important, not the location) to get the normal vector to the plane, and you also have a point on the plane (or several given your line equation).

    Do you know the normal equation that relates a plane normal with a general point on the plane with a specific known point on the plane?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2011
    Posts
    83

    Re: Equation of a plane in normal form ( with 2 lines)

    Do you mean I should cross multiply those two vectors
    With the basis vectors e1,e2,e3?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Equation of a plane in normal form ( with 2 lines)

    Yes, if you multiply the two direction vectors (note the word direction), you'll get a normal vector to the plane and you can do this because one lies on the plane and the other is parrallel.

    The multiplication I refer to is the cross product.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2011
    Posts
    83

    Re: Equation of a plane in normal form ( with 2 lines)

    Ok so when I have got the normal, what's the next step?
    Ihave two points, how can I deal with the problem now?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Equation of a plane in normal form ( with 2 lines)

    The plane equation in linear form is n . (r - r0) = 0 where r is any point on the plane, r0 is a specific point and n is the normal. Have you gone throught this in class? If not I think that if they haven't mentioned it then you should go ask your lecturer/teacher.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 9th 2012, 12:09 PM
  2. Replies: 1
    Last Post: April 6th 2011, 08:03 AM
  3. [SOLVED] Vectors: Finding an equation for plane that contains the two lines
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 10th 2010, 09:19 PM
  4. Equation of plane from 2 lines
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2010, 02:11 AM
  5. Plane equation given parallel lines
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 24th 2009, 10:46 PM

Search Tags


/mathhelpforum @mathhelpforum