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Thread: Identifying points from lines

  1. #1
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    Question Identifying points from lines

    Hi,

    I hope someone can help.

    Identifying points from lines-screen-shot-2018-01-28-11.17.52-am.png

    I know that the direction vector for line 1 is (2,1,-1) and for line 2 is (3,2,-3).

    Not sure where to go from here.

    - otownsend
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  2. #2
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    Re: Identifying points from lines

    Quote Originally Posted by otownsend View Post
    Click image for larger version. 

Name:	Screen Shot 2018-01-28 at 11.17.52 AM.png 
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    I know that the direction vector for line 1 is (2,1,-1) and for line 2 is (3,2,-3).
    I don't know what the author of the questions wants you to do.
    But lines $L_1~\&~L_2$ are skew. It is well known that the is a unique perpendicular to each of two skew lines.
    Suppose that $L_1: A+tD~\&~L_2: B+sE$
    Using the hint, let $P\in L_1~\&~Q\in L_2$ So $\overrightarrow {PQ}$ will perpendicular to both $D~\&~E$.
    Moreover, $\overrightarrow {PQ}$ will parallel to $D\times E$.

    This is quite a tedious task. I don't envy you trying to juggle these ordinates.
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  3. #3
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    Re: Identifying points from lines

    $\overrightarrow {PQ}$ parallel to $D\times E$

    means

    $\overrightarrow {PQ} = \lambda D\times E$ for some real number $\lambda$

    that's a vector equation so we have three equations in three unknowns $t,s,\lambda $
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