Results 1 to 5 of 5
Like Tree2Thanks
  • 2 Post By earboth

Math Help - 3d vector

  1. #1
    Junior Member
    Joined
    Aug 2012
    From
    The Earth
    Posts
    71
    Thanks
    1

    3d vector

    Question: The position vectors of the points A, B and C referred to an origin O are 4i-3j-k and -8i+6j+5k respectively. If AB meets the z-axis at P, find the ratio AP:PB.

    What is mean by "If AB meets the z-axis at P" ?
    Can anyone explain to me please?
    And how do I solve it?

    Please help, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123

    Re: 3d vector

    Quote Originally Posted by alexander9408 View Post
    Question: The position vectors of the points A, B and C referred to an origin O are 4i-3j-k and -8i+6j+5k respectively. If AB meets the z-axis at P, find the ratio AP:PB.

    What is mean by "If AB meets the z-axis at P" ?
    Can anyone explain to me please?
    And how do I solve it?

    Please help, thanks.
    1. Stationary vector of C ( \vec c) is missing.

    2. AB is a straight line passing through A and B:

    AB: r = \langle 4,-3,-1 \rangle + t \cdot \langle 12, -9 ,-6 \rangle

    If this line has a common point with the z-axis the point P has the coordinates P(0,0,p)

    Determine p.

    3. When you finally have found P(0,0,1) calculate the distances |\overline{AP}| and |\overline{BP}| and determine the ratio of the distances. I've got \frac{|\overline{AP}|}{|\overline{BP}|} = \frac12
    Thanks from HallsofIvy and alexander9408
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2014
    From
    Malaysia
    Posts
    2

    Re: 3d vector

    how to determine the p? pls hlp me.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123

    Re: 3d vector

    Quote Originally Posted by almostSeeker View Post
    how to determine the p? pls hlp me.
    Good morning,

    take this equation:

    AB: r = \langle 4,-3,-1 \rangle + t \cdot \langle 12, -9 ,-6 \rangle

    and replace \vec r = \langle x,y,z \rangle

    Since P has the coordinates P(0,0,p) you'll get
    \begin{array}{lcr}0&=&4+12t \\ 0&=&-3-9t \\p&=&-1-6t\end{array}

    1. Use the 1st or the 2nd equation to determine t.
    2. Sub in this value into the 3rd equation to get the value of p.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2014
    From
    Malaysia
    Posts
    2

    Re: 3d vector

    thanks sir
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 24th 2012, 02:41 AM
  2. Replies: 8
    Last Post: January 11th 2011, 10:17 AM
  3. Replies: 2
    Last Post: January 27th 2010, 08:23 PM
  4. Replies: 11
    Last Post: December 23rd 2009, 01:30 AM
  5. Replies: 2
    Last Post: October 5th 2009, 03:25 PM

Search Tags


/mathhelpforum @mathhelpforum