Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By Plato

Math Help - Line and point in $\mathbb{R}^3$

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    Line and point in $\mathbb{R}^3$

    Let P_0 = (1,0,-2) and let \ell be the line that goes through P_1 = (1,1,1) and P_2 = (3,2,6). Find the coordinates for a point P on \ell such that P_0 and P are orthogonal to \ell.


    I try with taking (P_2 - P_1) \cdot (Q - P_0) = 0 (dot product = 0) but I end up wrong.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,964
    Thanks
    1008

    Re: Line and point in $\mathbb{R}^3$

    What is Q?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,386
    Thanks
    1476
    Awards
    1

    Re: Line and point in $\mathbb{R}^3$

    Quote Originally Posted by jacob93 View Post
    Let P_0 = (1,0,-2) and let \ell be the line that goes through P_1 = (1,1,1) and P_2 = (3,2,6). Find the coordinates for a point P on \ell such that P_0 and P are orthogonal to \ell.
    The line \ell(t)=(1+2t,1+t,1+5t) so P\in\ell means P=(1+2t,1+t,1+5t) for some t.

    So \overrightarrow {{P_0}P}  = \left( {2t,t, - 1 + 5t} \right).

    Find t such that \overrightarrow {{P_0}P} \cdot <2,1,5>=0
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    Re: Line and point in $\mathbb{R}^3$

    Quote Originally Posted by Plato View Post
    The line \ell(t)=(1+2t,1+t,1+5t) so P\in\ell means P=(1+2t,1+t,1+5t) for some t.

    So \overrightarrow {{P_0}P}  = \left( {2t,t, - 1 + 5t} \right).

    Find t such that \overrightarrow {{P_0}P} \cdot <2,1,5>=0
    I find \overrightarrow {{P_0}P} = P - P_0 = (1+2t,1+t,1+5t) - (1,0,-2)=(2t,1+t,3+5t).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    Re: Line and point in $\mathbb{R}^3$

    Quote Originally Posted by Plato View Post
    The line \ell(t)=(1+2t,1+t,1+5t) so P\in\ell means P=(1+2t,1+t,1+5t) for some t.

    So \overrightarrow {{P_0}P}  = \left( {2t,t, - 1 + 5t} \right).

    Find t such that \overrightarrow {{P_0}P} \cdot <2,1,5>=0
    I get t=-\frac{16}{30}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. \mathbb{Q}\times\mathbb{Q} is not cyclic
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 10th 2011, 01:22 PM
  2. Replies: 3
    Last Post: August 26th 2011, 06:59 PM
  3. Replies: 2
    Last Post: June 8th 2010, 04:59 PM
  4. Replies: 0
    Last Post: October 22nd 2009, 11:04 AM
  5. Replies: 3
    Last Post: February 20th 2008, 10:17 AM

Search Tags


/mathhelpforum @mathhelpforum