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Math Help - Help expressing distance in the following form...

  1. #1
    Senior Member Danneedshelp's Avatar
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    Help expressing distance in the following form...

    Show that in 3-space the distance d from a point p to the line l through points a and b can be expressed as d=\frac{|ap\times{ab}|}{|ab|}.

    I was asked this question by my girlfriend who is taking calculus three this summer. I took the class a couple semesters ago and cannot remember this stuff for the life of me. I'm refreshing now, so maybe I will get given a little more time, but for now I am pretty stuck.

    Any help would be appreciated.

    Thanks
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    Quote Originally Posted by Danneedshelp View Post
    Show that in 3-space the distance d from a point p to the line l through points a and b can be expressed as d=\frac{|ap\times{ab}|}{|ab|}.
    Recall that \sin (\phi ) = \frac{{\left\| {\overrightarrow {AP}  \times \overrightarrow {AB} } \right\|}}{{\left\| {\overrightarrow {AP} } \right\|\left\| {\overrightarrow {AB} } \right\|}} where \phi is the angle between \overrightarrow {AP}~\&~\overrightarrow {AB}.
    The distance is the length of a leg of a right triangle opposite \phi.
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