Results 1 to 2 of 2

Math Help - Shortest distance between a point and a line - Vectors

  1. #1
    Junior Member Fnus's Avatar
    Joined
    Nov 2006
    Posts
    48

    Shortest distance between a point and a line - Vectors

    I'd just like it if someone could tell me where it is I'm going wrong in my calculations.. It might even be at the very beginning, I'm at a loss. ):

    'Find the distance from the point P(3,0,-1) to the line with equation r=2i-j+4k+\lambda(3i+2j+k)'

    Any point on the line I got to be A(2+3\lambda,-1+2\lambda,4+\lambda).

    That means that \overline{PA}=\left(\begin{array}{cc}-1+3\lambda\\-1+2\lambda\\5+\lambda\end{array}\right), and the direction vector of the line is \overline{b}=\left(\begin{array}{cc}3\\2\\1\end{ar  ray}\right)

    Then I tried to calculate their scalar product to find when they are perpendicular and thus closest to each other, but then I got \lambda to be 0...

    So would someone please tell me where it is I go wrong?
    Is it something at the very beginning? ):

    And then another question that is very simple!
    What is the direction vector of the line 3x-y=4?
    A fixed point would be (0,-4), right?

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Suppose that P is a point not on the line \ell :Q + \lambda\overrightarrow d .
    Then distance D(\ell ,P) = \frac{{\left\| {\overrightarrow {QP}  \times \overrightarrow d } \right\|}}{{\left\| {\overrightarrow d } \right\|}}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 22nd 2013, 02:40 PM
  2. Replies: 1
    Last Post: April 22nd 2011, 12:22 AM
  3. Replies: 2
    Last Post: January 25th 2011, 04:46 AM
  4. Distance between point and line (vectors)
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 12th 2010, 07:49 AM
  5. Shortest distance between point and line
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: June 1st 2010, 12:48 AM

Search Tags


/mathhelpforum @mathhelpforum