Results 1 to 4 of 4

Math Help - Linear Algebra:Planes help

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    13

    Unhappy Linear Algebra:Planes help

    The example is :
    Convert the scalar equation 4x − 2y + z = 2 into a parametric form.
    This is not a big  deal, usually. We have the coefficients, 4, -2 and 1, so the normal is
    (4,−2,1)
    (4,−2,1)=2 it’s not = 0, so there will be 2 vectors orthogonal
    to it. Any two vectors that are not in the same direction will do. The best way to make sure they aren’t in the same direction is to make them cover different variables, i.e., use only x and y for one, y and z for the other.

    For instance,

    (1,2,0) is orthogonal to (4,−2,1) as is(0,1,2)
    Those are clearly not in
    the same direction. They’ll do. Recall that we need to match the right hand side. Any
    combination of those two will not change the total on the left. We just need a single point that matches. So,
    x =1/2-->(1/2,0,0)
    y=-1--->(0,-1,0)
    z=2--> ( 0,0,2)


    So, any will do, here’s one final set

    (xyz)=(1,1,0)+(1,2,0)t+(0,1,2)s

    From all this my questions are when they mention that the normal is (4,-2,1) they say that the orthogonal is (1,2,0) and (0,1,2).

    I was wondering how they got the orthogonal and how they got those two from the normal (4,-2,1)?

    My second question is how did they get the final set?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: Linear Algebra:Planes help

    If you want to find a parametric equation to Ax+By+Cz+D=0 follow these steps:

    1. find 3 points on the plane Ax+By+Cz+D=0 (you can take x=y=0, then find z\ Say that (A,B,C) is your normal then (A,B,C)(a,b,c)=0 )
    2. Suppose that 3 points are A, B and C. Create two vectors AB and AC.
    3. Construct your parametric equation: (point on a plane)+vec(AB)*t +vec(AC)*s
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,973
    Thanks
    1638

    Re: Linear Algebra:Planes help

    A much simpler way to arrive at parametric equations for a plane is to solve for one variable in terms of the other two:
    2x- y+ z= 2 is the same as z= 2- 2x+ y. So x= x, y= y, z= 2- 2x+ y are parametric equations for the plane. If you don't like the idea of using x and y as paramters, just "rename" them: x= s, y= t, z= 2- 2s+ t.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2011
    Posts
    13

    Re: Linear Algebra:Planes help

    I still don't understand what to do, so my original equation is 4x-2y+z=2 and i know the normal is 4,-2, 1 so what would i do to get it into parametric form? Are you able to give me an example of how to do this question?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 1st 2011, 10:00 PM
  2. Replies: 2
    Last Post: December 6th 2010, 03:03 PM
  3. Tangent Planes + Linear Approximation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 30th 2010, 05:10 AM
  4. Replies: 7
    Last Post: August 30th 2009, 10:03 AM
  5. Linear System: Phase Planes
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 23rd 2009, 07:30 AM

Search Tags


/mathhelpforum @mathhelpforum