Results 1 to 6 of 6

Math Help - Planes, lines, points

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    29

    Planes, lines, points

    One question, 3 parts

    A. Find an equation for the plane consisting of all points (x,y,z) that are equidistant from the points (-4,2,1) and (2,-4,3).

    B. Find the points A on the line with symmetric equations x=y=z and B on that with equations x+1=y/2=z/3 such that |AB| is the shortest distance between the two lines. Hence compute the shortest distance.

    C. Let L be the line of intersection of the two planes with equations x+2y-z=2 and 2x-y+4z=5. Find the point A on this line such that the distance from (0,0,0) to A is the shortest from 0 to L.

    needdd urgent helppp cant find solutions to these types of problems anywhere!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    626
    Hello, ramzouzy!

    Here's the first one . . .


    A. Find an equation for the plane consisting of all points P(x,y,z)
    that are equidistant from the points A(-4,2,1)\text{ and }B(2,-4,3).
    We want \overline{PA} \:= \:\overline{PB}.

    We have: . \begin{array}{ccc}\overline{PA} &=& \sqrt{(x+4)^2 + (y-2)^2 + (z-1)^2} \\\overline{PB} &=& \sqrt{(x-2)^2 + (y+4)^2 + (z-3)^2} \end{array}

    Hence: . (x+4)^2 + (y-2)^2 + (z-1)^2 \;=\;(x-2)^2 + (y+4)^2 + (z-3)^2

    . . x^2+8x+16 + y^2-4y+4+z^2-2z+1 \;=\;x^2-4x + 4 + y^2 + 8y + 16 + z^2-6z+9

    . . 12x - 12y + 4z \:=\:8\quad\Rightarrow\quad\boxed{3x - 3y + 2z \;=\;2}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2008
    Posts
    29
    anyone else for the other two parts plzzz??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    I will comment on the particular problem, #2. The problem is almost identical to one found in Stewarts’ Caculus. The difference is Steward asks students to find the distance between the two skew lines. That is an easy operation. But to find the particular points is rather difficult (maybe just long).
    Given two skew lines l_1 :r_1  + tD_1 \,\& \,l_2 :r_2  + tD_2 \, the distance between the two lines is given by \frac{{\left| {\left( {D_1  \times D_2 } \right) \cdot \left( {r_1  - r_2 } \right)} \right|}}{{\left\| {D_1  \times D_2 } \right\|}}.

    But finding A & B is a different matter.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2008
    Posts
    29
    i have both stewart single and multi variable book.. however i couldnt find the topic in the book... at some examples of the same questions or anything close to it...

    and regarding that formula, is that a generic formula for skew lines or is it derived and put into place for this situation only?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by ramzouzy View Post
    i have both stewart single and multi variable book.. however i couldnt find the topic in the book... at some examples of the same questions or anything close to it...
    and regarding that formula, is that a generic formula for skew lines or is it derived and put into place for this situation only?
    In Stewart 5e it is on page 867.
    The distance formula I gave you is what it is: the distance between two skew lines.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lines and Planes?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 8th 2011, 12:25 PM
  2. Lines and Planes in 3D
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 7th 2010, 01:45 AM
  3. Replies: 1
    Last Post: April 17th 2010, 11:52 PM
  4. Lines and Planes
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 1st 2010, 08:03 AM
  5. planes, lines and points type of question.
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: August 15th 2006, 06:54 AM

Search Tags


/mathhelpforum @mathhelpforum