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Math Help - Distance Between Two Lines?

  1. #1
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    Distance Between Two Lines?

    Let P=(5,2,4) , Q=(4,0,5) , R=(2,5,6) and S=(5,1,6) . Let L1 be the line passing through P and Q, and let L2 be the line passing through R and S.

    What is the distance between L1 and L2?
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  2. #2
    Pur
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    <br />
L_1=P+<br />
\begin{bmatrix}<br />
1 \\ 2 \\ 1<br />
\end{bmatrix}<br />
L_2=R+<br />
\begin{bmatrix}<br />
-3 \\ 6 \\ 0<br />
\end{bmatrix}<br />

    These lines are not parallel. Therefore we compute the distance as follows:
    <br />
D=\frac{|\vec{RP}\cdot(v_1\times v_2)|}{||v_1\times v_2||}<br />
    where v_1,v_2 are the direction vectors for the two lines.Thus the distance is calculated:
    <br />
D=\frac{15}{\sqrt{117}}<br />
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  3. #3
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    I did that, but it says that I'm incorrect.
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  4. #4
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    Ah nevermind, the magnitude of the normal is sqrt189, not 117. Thanks though, you were of great help!
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