Results 1 to 8 of 8

Math Help - Lines in a Plane 13

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    Lines in a Plane 13

    Find a vector equation for the line through the origin that intersects both of the lines r=(2,-16,19)+t(1,1,-4) and r=(14,19,-2)+u(-2,1,2).

    This is my work so far, but I can't seem to find the correct answer.

    d1=(1,1,-4)
    d2=(-2,1,2)

    i'm stuck here..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Let r=(0,0,0)+v(a,b,c) the requested line

    There exists a value for v, say v_1 and another value, say v_2 such that

    2+t=v_1a
    -16+t=v_1b
    19-4t=v_1c
    14-2u=v_2a
    19+u=v_2b
    -2+2u=v_2c

    Let x = \frac{v_2}{v_1}

    14-2u=x(2+t)
    19+u=x(-16+t)
    -2+2u=x(19-4t)

    Solving gives
    x = -\frac{64}{9}
    u = 41
    t = \frac{121}{16}

    You can chose one of the coordinates a, b or c
    If you chose a = 17 then b = -15 and c = -20
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2008
    Posts
    425
    how did you get a=17?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Nov 2008
    Posts
    425
    I can't seem to figure out how you got your final answer, the a=17 then b=-15 and c =-20.. this step before this, or to get to this a=17, where did it come from?

    Can you, running-gag, or someone else clarify it for me? please and thank you
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    As I said before you can chose any value for a
    I have chosen a=17 because it makes the other values very simple

    The coordinates of the intersect with r=(2,-16,19)+t(1,1,-4) is given for t=121/16, therefore (153/16,-135/16,-180/16)

    If you chose a=17, you will get b=-15, c=-20 and v1=9/16
    But if you chose a=34, you will get b=-30, c=-40 and v1=9/32

    This does not change the coordinates of the intersect (v1a,v1b,v1c) and does not change either the line since r=(0,0,0)+v(17,-15,-20) and r=(0,0,0)+v(34,-30,-40) are the same line
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Nov 2008
    Posts
    425
    ok, so i could even choose a=1 and then find v1, and then find b and c right?
    so
    a=1
    v1=153/16

    b=-135/153

    c=-180/153
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Nov 2008
    Posts
    425
    running-gag? can you let me know about what i said above? just this last question

    Thanks so much for your help by the way
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    That's correct !
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lines in a Plane 7
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 6th 2009, 11:25 AM
  2. Lines in a Plane 7
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 6th 2009, 04:40 AM
  3. Lines in a Plane 13
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 5th 2009, 11:22 PM
  4. Lines in a Plane 14
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 5th 2009, 06:14 PM
  5. n lines in a plane
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 21st 2008, 10:59 AM

Search Tags


/mathhelpforum @mathhelpforum