Results 1 to 6 of 6

Math Help - Vector ratio problem

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    60

    Vector ratio problem

    The point C has position vector (2 3) and point D has position vector (1 2).Find the position vector of the point which divides CD in the ratio 4:-3

    I recognized that the minus sign in 4:-3 indicates that it divides the line externally.However,i'm not able to get the ratios right when solving the problem.Can anyone show me with a diagram,the way the ratio is distributed in the line? (< i guess this is where i get it wrong?the ratio part)
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by kandyfloss View Post
    The point C has position vector (2 3) and point D has position vector (1 2).Find the position vector of the point which divides CD in the ratio 4:-3

    I recognized that the minus sign in 4:-3 indicates that it divides the line externally.However,i'm not able to get the ratios right when solving the problem.Can anyone show me with a diagram,the way the ratio is distributed in the line? (< i guess this is where i get it wrong?the ratio part)
    Thanks
    Dear kandyfloss,

    Hope this will help you. If you need any clarifications please don't hesitate to reply me.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2010
    Posts
    60
    I'm still a bit confused with the ratio..can you solve the problem and show me?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by kandyfloss View Post
    I'm still a bit confused with the ratio..can you solve the problem and show me?
    Dear kandyfloss,

    Can you explain about what confuses you? If the point that divides CD externally is E(x,y), you can write,

    1=\frac{x+(3\times{2})}{4} ; considering D divides CE internally

    2=\frac{y+(3\times{3})}{4}

    Hence you can find the point E.

    Hope this will help you.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Dividing a line segment externally

    Hello kandyfloss
    Quote Originally Posted by kandyfloss View Post
    The point C has position vector (2 3) and point D has position vector (1 2).Find the position vector of the point which divides CD in the ratio 4:-3

    I recognized that the minus sign in 4:-3 indicates that it divides the line externally.However,i'm not able to get the ratios right when solving the problem.Can anyone show me with a diagram,the way the ratio is distributed in the line? (< i guess this is where i get it wrong?the ratio part)
    Thanks
    You're right in saying that the point divides the line segment CD externally. If CP:PD = 4 :-3, then the ratio of the distances CP and PD is 4:3, but they are in opposite directions (hence the minus sign). So, from C we shall go out 4 'lengths' to get to P and then come back 3 'lengths' to D.

    Take a look at the diagram I've attached. You'll see that:
    CP:PD = 4:-3
    Now you probably know that the position vector of the point dividing the line joining the points with position vectors \vec a and \vec b in the ratio \lambda:\mu is:
    \frac{\mu\vec a + \lambda \vec b}{\lambda + \mu}
    So the point that divides CD in the ratio 4:-3 has position vector:
    \frac{-3\vec c + 4\vec d}{4-3}
    =-3\binom23+4\binom12

    =\binom{-6}{-9}+\binom48


    =\binom{-2}{-1}

    I hope that clears things up.

    Grandad
    Attached Thumbnails Attached Thumbnails Vector ratio problem-untitled.jpg  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Apr 2010
    Posts
    60
    Yes,that's much more clear now.Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ratio problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 30th 2009, 07:40 AM
  2. Ratio problem.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 2nd 2009, 08:22 PM
  3. Replies: 2
    Last Post: February 7th 2009, 11:31 PM
  4. Another ratio problem..
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 6th 2007, 05:20 PM
  5. Ratio problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 19th 2007, 05:52 PM

Search Tags


/mathhelpforum @mathhelpforum