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Homework Help: Find Find the point in this plane where it intersects the z axis

  1. Sep 26, 2011 #1
    1. The problem statement, all variables and given/known data

    find the point in this plane where it intersects the z axis (x=y=0).

    P = {<x;y;z;> = <1;-1;0;> + a<1;-2;0;> + b<2;0;-1;> , for all a,b}

    (by <l;m;n;> i mean to denote a column)

    2. Relevant equations

    3. The attempt at a solution
    I talked to my TA last friday and he made it seem easy, but I don't remember what he said anymore. I have something that looks like

    I set up a matrix that looks like

    [<1;-1;0;> <1;-2;0;> <2;0;-1;>] [<1;a;b>] = [<0;0;2;>]

    I'm not really sure what to do from here. It says it is asking for a point, does this mean which (a,b) works? What can you help me with?

    Thanks in advance.
  2. jcsd
  3. Sep 26, 2011 #2


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    find (a,b) where it works by row-reducing your matrix

    then use (a,b) in
    P= P(a,b)=<x,y,z>=<x(a,b),y(a,b),z(a,b)>

    a & b are parameters in the parameterisation of the plane, each (a,b) corresponds to a point <x,y,z> on the plane P
  4. Sep 26, 2011 #3


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    This is all you should need.
    <x;y;z;> = <1;-1;0;> + a<1;-2;0;> + b<2;0;-1;> ​

    It says that
    x = 1 + 1∙a + 2∙b

    y = -1 - 2∙a + 0∙b

    z = 0 + 0∙a - 1∙b

    Now "Find the point in this plane where it intersects the z axis (x=y=0)." So, find what a & b make this happen?

    Edited per ehild's note.

    Thanks goes to ehild.
    Last edited: Sep 27, 2011
  5. Sep 27, 2011 #4


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    There is a typo in your equations (shown in red)

    It should be

    y=-1-2∙a +0∙b

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