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Math Help - Vector-Valued Lines

  1. #1
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    Vector-Valued Lines

    Urgent! Please help soon! Here's the equation:

    Find the distance between the lines:

    r1(t) = (1,2,3) + t(0,-1,2)
    r2(t) = (0,1,1) + t(1,1,0)

    So far all I've been able to figure out is conversions to unit vector i, j, and k:

    r1(t) = 0i + 1 -j +2 +2k +3 = -j + 2k + 6
    r2(t) = i + j + 1

    But here I hit a block....please help!
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  2. #2
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    Re: Vector-Valued Lines

    Hey nrr5094.

    You need to find a vector which is perpendicular to both lines (Hint: think about the cross product of the directional vectors of each line)
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  3. #3
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    Re: Vector-Valued Lines

    Quote Originally Posted by nrr5094 View Post
    Find the distance between the lines:
    r1(t) = (1,2,3) + t(0,-1,2)
    r2(t) = (0,1,1) + t(1,1,0)
    If the two lines are are parallel chose a point on one of them and then find the distance of it to the other line.

    In general, let say two lines \left\{ {\begin{array}{*{20}c}   {\ell _1 :P + tD_1 }  \\   {\ell _2 :Q + tD_2 }  \\ \end{array} } \right. then D\left( {\ell _1 ,\ell _2 } \right) = \frac{{\left| {\left( {P - Q} \right) \cdot \left( {D_1  \times D_2 } \right)} \right|}}{{\left\| {D_1  \times D_2 } \right\|}}
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