Results 1 to 2 of 2

Math Help - 3D vectors

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    Guam
    Posts
    2

    3D vectors

    Given points A and B in 3-dimensional space, describe the solutions to
    −→ −→
    P A P B = 0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,719
    Thanks
    635

    Re: 3D vectors

    Hello, romean2015!

    \text{Given points }A\text{ and }B\text{ in 3-space, describe the solutions to: }\overrightarrow{PA}\cdot\overrightarrow{PB}=0

    Consider a sphere with AB as its diameter.
    Consider any point P on this sphere.
    Draw chords PA and PB.
    Code:
                  * * *
              *           *  P
            *               o
           *                 *
    
          *                   *
        A o - - - - * - - - - o B
          *                   *
    
           *                 *
            *               *
              *           *
                  * * *
    \text{Since }\angle APB = 90^o,\,\text{ then: }\,\overrightarrow{PA}\cdot\overrightarrow{PB} \,=\,0

    \text{Therefore, the locus of point }P\text{ is the sphere with diameter }AB.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 15th 2011, 05:10 PM
  2. Replies: 3
    Last Post: June 30th 2011, 08:05 PM
  3. Replies: 2
    Last Post: June 18th 2011, 10:31 AM
  4. [SOLVED] Vectors: Finding coefficients to scalars with given vectors.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 23rd 2011, 12:47 AM
  5. Replies: 4
    Last Post: May 10th 2009, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum